Defendants-appellants, Chen Xiang (“Chen”) and Lin Xian Wu (“Lin”) (collectively, “Appellants”), appeal from judgments of conviction entered in the United States District Court for the Southern District of New York (Casey, /.), following a jury trial, convicting each of the Appellants, under a superseding indictment, of one count of conspiracy to commit extortion, in violation of 18 U.S.C. § 1951 (“Count One”); one count of extortion, in violation of 18 U.S.C. §§ 2 and 1951 (“Count Two”); three counts of conspiracy to commit robbery, in violation of 18 U.S.C. § 1951 (“Counts Four, Seven, and Ten”); three counts of robbery, in violation of 18 U.S.C. §§ 2 and 1951 (“Counts Five, Eight, and Eleven”); and four counts of using, carrying, and possessing a firearm during and in relation to participation in the charged extortion, robberies, and conspiracies to commit extortion and robbery, in violation of 18 U.S.C. § 924(c)(1)(A)(ii) (“Counts Three, Six, Nine, and Twelve”).
Appellants contend that the evidence adduced at trial to prove their guilt in connection with the charged counts of extortion and of conspiracy to commit extortion *365was insufficient as a matter of law. We agree and, accordingly, reverse the convictions of Appellants under Counts One and Two. Appellants also contend that as a consequence of the legal insufficiency of the extortion-related evidence, the convictions of Appellants for using, carrying, and possessing a firearm during and in relation to the charged extortion and conspiracy to commit extortion also must be reversed. We agree with Appellants in this regard, too, and accordingly reverse the convictions of Appellants under Count Three.1 Finally, in view of these reversals, we remand for resentencing. We , affirm the judgments of the District Court in all other respects.
BACKGROUND
On August 12, 2002, Appellants were charged in a superseding indictment (the “Indictment”) as follows: Count One charged Appellants with' conspiring to commit extortion, in violation of 18 U.S.C. § 1951. Count Two charged Appellants with extortion, in violation of §§ 2 and 1951. Count Three charged Appellants with using a firearm during and in relation to the crimes charged in'Counts One and Two, in violation of § 924(c)(1)(A)(ii). Counts Four, Seven, and Ten charged Appellants with conspiring to commit robbery, in violation of § 1951. Counts Five, Eight, and Eleven charged Appellants with robbery, in violation of §§ 2 and 1951. And finally, Counts Six, Nine, and Twelve charged Appellants with using a firearm during and in relation to the crimes charged in Counts Four, Five, Seven, Eight, Ten, and Eleven, in violation of § 924(c)(l)(A)(ii).
A. Underlying Criminal Conduct
The charges in the Indictment have their genesis in a series of robberies and related incidents that occurred in Manhattan’s “Chinatown” during a six-month period between the summer of 2001 and the early months of 2002.2 The first such incident occurred in or around July 2001 at 75’ Eldridge Street — an illegal gambling parlor located behind a clothing store.3 *366On or about July 23, 2001, at approximately 6:00 p.m., an unknown caller telephoned Chen Tin Hua (“Hua”), a “shareholder” in the gambling operation, and identified himself as being associated with “Vietnamese Boy” — presumably, co-defendant/cooperating witness Xiao Qin Zhou (“Xiao”). The caller stated that Vietnamese Boy would come to the gambling parlor later that day to pick up $10,000, which the caller instructed Hua to place in a red envelope. Hua told the caller that he had no money and hung up.
Later that evening, while in the parlor, Hua was summoned outside by a group of men demanding to speak with him. Awaiting Hua were Appellants — Chen and Lin — along with Xiao and co-defendant Li Wei. All four pointed guns at Hua, and Xiao demanded that he give them $10,000. Hua told the group that he had no money. Xiao struck Hua on the head, and Li Wei, using his gun, struck Hua in the stomach. Xiao then ripped a necklace from around Hua’s neck, and the group fled the scene in a vehicle.
Following this foray, the gang began to terrorize the neighborhood systematically. On or about September 30, 2001, Appellants, together with Xiao and co-defendant Li Xin Ye, robbed an illegal gambling parlor located at the back of a barbershop at 21 Eldridge Street, again using guns, and this time making off with more than $10,000.
On or about November 21, 2001, Chen, Lin, Xiao, and co-defendants Chun Rong Chen and Hing Wah Gau attempted to rob the illegal gambling parlor at 75 Eldridge Street but failed because they could not gain entry. Later that same day, the same gang succeeded in robbing another such parlor — this one located inside a florist shop at 109 East Broadway. The five had split up earlier in the day, and only Chen, Xiao, and Chun Rong Chen actually entered the 109 East Broadway gambling parlor during the robbery. Afterwards, however, the five gangsters reconvened and split the $3000 “take” from the robbery.
Finally, on January 23, 2002, Appellants, Xiao, and co-defendant Lin Li robbed an illegal gambling parlor located at the back of a barbershop at 85 Allen Street. Chen and Lin Li entered the gambling parlor first, followed by Lin and Xiao. Appellants and Lin Li, brandishing guns, announced a robbery and the four then proceeded to make off with approximately $10,000. During the robbery, Lin Li pistol-whipped one of the victims in the head.
B. Pre-Trial Proceedings
Prior to trial, the Government moved to admit the testimony of Xiao, Chun Rong Chen, and Li Xin Ye that, between 2000 and 2002, they participated with Appellants in fourteen robberies that were not charged in the Indictment. The Government offered the testimony to demonstrate the criminal relationships among the Appellants and the cooperating witnesses. The Government also sought to introduce *367this evidence, pursuant to Federal Rule of Evidence Rule 404(b), to prove Appellants’ knowledge, intent, preparation, and plan. Appellants did not object to any of the purposes for which the Government offered the evidence of the prior acts, but sought to exclude the evidence on the grounds that the probative value of the evidence was substantially outweighed by its potential for prejudice. Appellants argued (i) that the evidence would “convince the jury of [Appellants’] propensity to commit crimes and lead [the jury] to ‘punish the bad m[e]n’ rather than deliberate upon the facts of the charged crime” and (ii) that “the danger of the jury inferring ‘propensity’ to commit the same kind of criminal acts as those charged [was] just to[o] great to justify admission for the purposes set forth by the [Government.”
Thereafter, the Government, “in an effort to streamline the trial,” amended its motion so as to request admission of evidence relating to only six of the fourteen prior acts.4 The Government also sought to introduce the plea allocution of co-defendant Li Wei — as a statement against penal interest, pursuant to Federal Rule of Evidence 804(b)(3) — to prove the existence of the extortion conspiracy charged in Count One of the Indictment. Chen objected to the admission of the plea allocution on Rule 403 grounds. At a conference held on May 15, 2003, the District Court heard argument oh the Government’s motion to admit the six prior uncharged crimes and the plea allocution of Li Wei, and on the motions of Appellants to preclude certain evidence.
On May 16, 2003, in a six-page unpublished Memorandum Decision and Order, the District Court denied the preclusion motions of Appellants and granted the Government’s motion to admit (i) the plea allocution of Li Wei and (ii) evidence of the prior uncharged crimes. Regarding the plea allocution, the District Court noted that Li Wei had already been sentenced and that, if. asked to testify, he would assert his Fifth Amendment privilege. Thus, the court found, Li Wei was unavailable within the meaning of Federal Rule of Evidence 804. Moreover, the court found, a plea allocution qualified as a declaration against penal interest under Rule 804.
Regarding the uncharged-crimes evidence, the court found that the prior uncharged crimes were no more inflammatory than the crimes charged in the Indictment and, moreover, would not have a cumulative effect because the Government sought “to introduce evidence of uncharged crimes that occurred a short period before the charged crimes and [that] were therefore part of the same transaction or series of events.” The court found that the crimes were “remarkably similar” to the charged crimes but that, “[flnasmuch as there [was] any prejudice to defendants, it [was] outweighed by the probativeness [sic] of the uncharged crimes evidence.” The court further found that the Government intended to use the facts of the uncharged crimes “as background evidence of the circumstances surrounding the events or to furnish an explanation of the understanding or intent with which certain' acts [had been] performed,” both of which were deemed permissible. Finally, the court found *368that any “danger of prejudice [could] be minimized by the use of a limiting 'instruction to the jury.”
C. Lin’s Mental Competence
On October 25, 2002, Lin moved the District Court, pursuant to 18 U.S.C. § 4244(a), for a hearing to determine his mental condition, on the ground that there was “reasonable cause to believe that [he was] suffering from a me[n]tal disease or defect for the treatment of which he [was] in need of custody for care or treatment in a suitable facility.” Lin also requested, pursuant to 18 U.S.C. § 4244(b), that he be given “a psychiatric or psychological examination” prior to the hearing. Between February 13 and March 28, 2003, in accordance with an order of the District Court, a “forensic mental health evaluation” of Lin was conducted by Dr. Thomas Pate-naude, a forensic psychologist affiliated with the Devens Federal Medical Center— a facility operated by the U.S. Department of Justice, Federal Bureau of Prisons (“BOP”) — in Ayer, Massachusetts. The goal of the evaluation was to determine whether Lin was “suffering from a mental disease or defect for the treatment of which he [was] in need of custody for care or treatment in a suitable facility.” Dr. Patenaude reported “with reasonable psychological certainty” that Lin was not suffering from such a mental disease or defect. The District Court made no further orders before trial with respect to Lin’s mental condition.
On or about December 18, 2003, subsequent to Lin’s trial, conviction, and appeal, the District Court received a letter from the BOP stating that an internal investigation had revealed “sufficient evidence to question the credibility and accuracy of [Dr. Patenaude’s] psychological evaluation” of Lin. On February 13, 2004, Lin moved this Court to stay his appeal and remand the case to allow him to seek an order from the District Court “for a new psychological evaluation.” On April 1, 2004, this Court granted that motion. On July 19, 2004, the District Court granted a second examination but, over Lin’s objection, ordered that Lin be evaluated by “an examiner to be designated by the [BOP],” rather than “by [Lin’s] chosen examiner.” Between July 30 and August 26, 2004, Dr. Randall Rattan, a forensic psychologist affiliated with the BOP, conducted a psychological evaluation of Lin at the Federal Medical Center in Fort Worth, Texas. After examining Lin and the records associated with his case, Dr. Rattan’s opinion was that Lin “appeared competent for both trial and sentencing.”
D. Trial and Sentence
The evidence’ at trial established that Appellants had, as part of a gang, engaged in a series of crimes during the approximately six-month period from July 2001 to January 2002. The Government’s evidence at trial consisted of testimony from cooperating witnesses Xiao, Li Xin Ye, and Chun Rong Chen — who, as noted above, were co-defendants and part of the gang that committed the crimes charged. The Government’s witnesses also included victims of the crimes, as well as law enforcement officers who were involved in the investigation of the gang’s activities. The Government also introduced physical evidence, including guns and ammunition, recovered from an apartment that Appellants had shared with a co-conspirator.
On May 29, 2003, after a two-week trial, a jury found both Chen and Lin guilty of each of the charged offenses. On September 18, 2003, the District Court sentenced Chen to a term of imprisonment of seventy months on Counts One, Two, Four, Five, Seven, Eight, Ten, and Eleven, to be followed by an aggregate consecutive term of *369imprisonment of 984 months on Counts Three, Six, Nine, and Twelve.5 The District Court ordered that Chen’s term of imprisonment be followed by concurrent terms of supervised release of three years on each count, and imposed a mandatory special assessment of $1200.
On September 25, 2003, the District Court sentenced Lin to a term of imprisonment of fifty-seven months on Counts One, Two, Four, Five, Seven, Eight, Ten, and Eleven, to be followed by an aggregate consecutive term of imprisonment of 984 months on Counts Three, Six, Nine, and Twelve. The District Court ordered that Lin’s term of imprisonment be followed by concurrent terms of supervised release of three years on each count, and imposed a mandatory special assessment of $1200. Judgments were entered in due course, and these timely appeals followed.
On appeal, Appellants challenge as unduly prejudicial the admission at trial of evidence of the six prior uncharged crimes; Appellants also challenge, on Confrontation Clause grounds, the admission of evidence relating to Li Wei’s plea allo-cution. In addition, Appellants assert that the evidence of their guilt with respect to the extortion-related counts was legally insufficient, regardless of the admissibility of any particular evidence and, therefore, that the convictions of Appellants under Counts One and Two must be reversed. Appellants also assert that, as a consequence of this insufficiency, the convictions of Appellants under Count Three— for using a firearm in connection with the extortion-related crimes — must also be reversed. Finally, Lin challenges the District Court’s denials of his requests to be examined by an independent psychologist and to have a competency hearing.6
DISCUSSION
I. Sufficiency of the Evidence
As noted above, Appellants contend that the evidence adduced at trial was insufficient to sustain the convictions of Appellants on the extortion-related crimes charged in Counts One and Two and, concomitantly, on the firearm crime charged in Count Three. The standard under which we review a challenge to the sufficiency of the evidence in a criminal trial is familiar:
Á defendant challenging a conviction based on a claim of insufficiency of the evidence bears a heavy burden. The evidence presented at trial should be viewed in the light most favorable to the Government, crediting every inference that the jury might have drawn in favor of the Government. We consider the *370evidence presented at trial in its totality, not in isolation, but may not substitute our own determinations of credibility or relative weight of the evidence for that of the jury. We defer to the jury’s determination of the weight of the evidence and the credibility of the witnesses, and to the jury’s choice of the competing inferences that can be drawn from the evidence. Accordingly, we will not disturb a conviction on grounds of legal insufficiency of the evidence at trial if any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.
Bruno, 383 F.3d at 82 (quoting Dhinsa, 243 F.3d at 648-49 (citations and internal quotation marks omitted)).
A. The Crimes Charged
Appellants were charged in Counts One through Three of the Indictment, respectively, as follows:
[Chen Xiang and Lin Xian Wu] unlawfully, willfully and knowingly combined, conspired, confederated and agreed together and with each other to commit extortion, as the term is defined in [18 U.S.C. § 1951(b)(2)], by conspiring to obtain property from and with the consent of others, to wit, occupants of a business located at 75 Eldridge Street, New York, New York, which consent would be and was induced by the wrongful use of actual and threatened force, violence and fear ....
[Chen Xiang and Lin Xian Wu] unlawfully, willfully and knowingly did commit extortion, as that term is defined in [18 U.S.C. § 1951(b)(2) ], and did attempt so to do, by the obtaining of property from and with the consent of others, to wit, occupants of a business located at 75 Eldridge Street, New York, New York, which consent was induced by the wrongful use of actual and threatened force, violence and fear ....
[Chen Xiang and Lin Xian Wu] unlawfully, willfully and knowingly used, carried and brandished a firearm during and in relation to ... the crimes charged in Counts One and Two of this Indictment.
B. The Essential Elements
In order to prove a conspiracy in violation of 18 U.S.C. § 1951 (“the Hobbes Act”), the Government must show that two or more persons entered into an agreement to commit the substantive offense as charged. See. e.g., United States v. Clemente, 22 F.3d 477, 480 (2d Cir.1994) (holding that conspiracy under the Hobbes Act requires proof of an agreement but that no overt act need be shown). “In order to convict a given defendant of conspiracy, the [G]overnment must prove that he knew of the conspiracy and joined it with the intent to commit the offenses that were its objectives, that is, with the affirmative intent to make the conspiracy succeed.” United States v. Ceballos, 340 F.3d 115, 123-24 (2d Cir.2003) (citations omitted).
“The agreement that is the gist of conspiracy may be tacit rather than explicit .... ” Ceballos, 340 F.3d at 124. “However, knowledge of the existence and goals of a conspiracy does not of itself make one a coconspirator.” Id. (internal quotation marks omitted); see, e.g., Direct Sales Co. v. United States, 319 U.S. 703, 711, 63 S.Ct. 1265, 87 L.Ed. 1674 (1943) (holding that the essence of a conspiracy is not mere knowledge of another’s illegal purpose, but the intent to “further, promote[,] and cooperate in it”). In other words, the defendant’s “ ‘attitude towards the forbidden undertaking must be more positive,’ ” United States v. Cianchetti, 315 F.2d 584, 588 (2d Cir.1963) (quoting United States v. *371Falcone, 109 F.2d 579, 581 (2d Cir.1940), aff'd 311 U.S. 205, 61 S.Ct. 204, 85 L.Ed. 128 (1940)); he must somehow have made “an affirmative attempt to further its purposes,” id.; accord Ceballos, 340 F.3d at 124.
Here, the object of the alleged conspiracy was to commit extortion, which, in the context of federal crimes, in relevant part, “means the obtaining of property from another, with, his consent, induced by wrongful use of actual or threatened force, violence, or fear.” 18 U.S.C. § 1951(b)(2) (emphasis added). Extortion is frequently exemplified by “revenue-producing measures ... utilized by organized crime to generate income”—measures “such as shakedown rackets and loan-sharking.” United States v. Nardello, 393 U.S. 286, 295, 89 S.Ct. 534, 21 L.Ed.2d 487 (1969).7 Of course, another familiar form of extortion is blackmail—where, for example, the extortioner obtains money from the victim by threatening to expose private or embarrassing conduct. See id. at 295-96, 89 S.Ct. 534 (describing how the extortioner threatened to expose the alleged homosexuality of the victims).
Choice on the part of the victim is a common theme in all extortion cases. As noted above, “the Hobbs Act definition of coercion speaks of obtaining property from another ‘with his consent.’ ” United States v. Arena, 180 F.3d 380, 394 (2d Cir.1999). Indeed, “[t]he legislative history of the Act makes clear that its proponents understood extortion to encompass situations in which a victim is given the option of relinquishing some property immediately or risking unlawful violence resulting in other losses, and he simply chooses what he perceives to be the lesser harm.” Id. at 395 (emphasis added) (citing 91 Cong. Rec. 11,904, 11,907 (discussing decision of business owner to pay tribute to extortionists rather than risk the physical destruction of his trucks: “The man pays the money to save himself and his property.”)). “In order to foreclose any argument by an extortionist that the relinquishment of property in such circumstances was [truly] voluntary, [however,] the Hobbs Act definition of extortion simply prohibits the extortionist from forcing the victim to make such a choice.” Id.
At bottom, undeniably, the victim of an extortion acts from fear, whether of violence or exposure. But both the language of the statute and the relevant precedents make clear that he or she always retains some degree of choice in whether to comply with the extortionate threat, however much of a Hobson’s choice that may be. Indeed, this element of consent is the razor’s edge that distinguishes extortion from robbery, which, in contrast, is defined in pertinent part as
the unlawful taking or obtaining of personal property from the person or in the presence of another, against his will, by means of actual or threatened force, or violence, or fear of injury, immediate or future, to his person or property, or property in his custody or possession, or the person or property of a relative or member of his family or of anyone in his company at the time of the taking or obtaining.
18 U.S.C. § 1951(b)(1) (emphasis added).
Among the essential elements of the federal crime of extortion, then, are (i) the defendant’s “use of actual or threatened force, violence, or fear,” and (ii) the *372victim’s consent — however forced — to the transfer of the property. 18 U.S.C. § 1951(b)(2). And concordantly, essential to a determination of conspiracy to commit extortion are (i) an agreement to use actual or threatened force to obtain property with the consent of the victim and (ii) actions taken in affirmative furtherance of that agreement. See Cianchetti, 315 F.2d at 588 (reversing conviction for conspiracy to violate drug law because “there was no fixed agreement to cooperate” and defendant “did noting to further the success of the enterprise”).
Here, the Government’s theory is that Appellants conspired to extort — and in fact committed extortion, and not robbery— when they “informed Hua by telephone that [Xiao] was coming to the gambling parlor to collect $10,000 from him,” instructing him to leave the money for Xiao’s pick-up in a red envelope, and, later, when they “summoned Hua outside the parlor and attempted to collect the money that had been demanded in the extortionate telephone call.” The Government contends that “[t]his call clearly represented a request, albeit under duress, for the money, rather than a forcible taking.” “After all,” the Government observes, “robbers typically do not telephone in their requests to victims ahead of time.” In making this distinction between robbery and extortion, however, the Government fails to identify any element of “duress,” either express or implied, in the telephone call, thus calling into question whether the Government has proved each and every element of the extortion-related crimes charged in the Indictment, as required by fundamental precepts of our law.8
C. The Evidence Presented
Here, the Government sought to prove the extortion-related charges primarily through the testimony of Xiao, a co-defendant and cooperating witness, and of Hua, the victim of the gang’s criminal conduct at 75 Eldridge Street. Hua, too, was cooperating with the Government — in his case, to avoid prosecution for his involvement in the gambling operation, for entering and working illegally in the United States, and for failure to report income.
Regarding the at-issue crime(s) committed at 75 Eldridge Street on July 23, 2001, Xiao — who, as detailed above, played a key role in all of the charged crimes — testified as follows:
Q. When did you first talk with the defendants about doing the robbery at 75 Eldridge Street?
A. On [July 23, 2001],
Q. Other than you, Ah Oo[,] and Yi Soon Gang, was anybody else participating in the conversation at your apartment about doing a robbery at 75 Eldridge Street?9
A. No.
Q. Of the three of [you — you, Ah Oo, and Yi Soon Gang — who] brought up the idea of robbing the gambling parlor at 75 Eldridge Street?
A. AhOo.
Q. What did Ah Oo say to you about this?
A. He said there is someone up there who could open up the door and we could go there to do the robbery.
*373Q. Did anyone else agree to do that robbery with the three of you?
A. Yes.
Q. Who?
A. Yi Guan.
Q. Where did you, Ah Oo[,] and Yi Soon Gang meet Yi Guan to go to 75 Eldridge Street?
A. Brooklyn.
Q. How did the four of you travel to 75 Eldridge Street?
A. We drove.
Xiao further testified that the four men — Appellants, Xiao, and Li Wei — drove together to 75 Eldridge Street, at approximately “five o’clock to seven o’clock.”10 He stated that they had attempted to gain entrance to the gambling parlor, but had been prevented from doing so by someone standing watch outside.
The testimony continued:
Q. And what happened after you were refused entry to the ... gambling parlor by the watch person?
A. A boss was called to come outside. [Hua then came outside.]
Q. Where were the four of you when you had that conversation with the boss of the gambling parlor?
A. Outside the door.
Q. The door to 75 Eldridge?
A. [Yes],
Q. What did you say to that boss of the gambling parlor?
A. Do you have any money on you? Why can’t we ... go inside?
Q. What, if anything, did the boss say back to you?
A. He did not answer.
Q. Did he give you any money at that time?
A. No.
Xiao further testified that all four had guns with them. Chen waved his gun, and Li Wei poked Hua in the stomach with his gun.
The testimony continued:
Q. As [Li Wei] was poking the boss’ stomach with his gun, did you hear [Li Wei] say anything at that time?
A. You believe me, I will kill you.
Q. What, if anything, did you do to the owner when he did not give you any money?
A. Yes, I slammed him on the face and I grabbed his necklace.
Q. What did you do with the necklace as you grabbed it?
A. I took it.
Q. What happened next?
A. We then drove home.
Hua, the victim of the 75 Eldridge Street crime, testified as follows regarding the above-noted telephone call that he received on July 23, 2001:
Q. Did you receive any telephone calls at the gambling parlor on July 23, 2001?
A. Yes.
Q. How many telephone calls did you receive that day?
A. One call.
Q. Approximately what time was it that you received that one telephone call?
A. At around six something.
*374Q. Is that in the afternoon, early evening?
A. In the evening.
Q. Was the caller male or female?
A. A male.
Q. Did he identify himself by name?
A. He did. He identified himself as Vietnamese [B]oy, 11 and he demanded money from me.
Q. What language did he speak?
A. In Foo Chow.
Q. And what specifically did he say to you?
A. He said Vietnamese [B]oy, he will come over to me to pick up money and I should give him $10,000.
Q. Did the caller say, Vietnamese [B]oy will come and pick up the money or did the caller say, I, Vietnamese [B]oy, will come and pick up money?
A. No. He said Vietnamese [B]oy will come and pick it up.
Q. Did he say anything about how Vietnamese [B]oy [would] pick up that money?
A. He said that I should put it in the red envelope, $10,000 worth, inside the red envelope.
Q. What, if anything, did you say to the caller?
A. I said I have no money.
Q. Did the caller say anything back to you at that point?
A. No. I h[u]ng up the phone.
Hua further testified that four individuals came to 75 Eldridge Street at approximately 8:00 p.m. on July 23, 2001. These individuals asked another employee of the gambling parlor to summon Hua outside. When Hua went outside, four individuals were waiting, pointing guns at him. Thereafter, Xiao, aka “Vietnamese Boy,” asked Hua for $10,000. When Hua said that he had no money, one of the other men poked Hua in the side with his gun, and Xiao hit Hua on his head. Xiao then ripped the necklace from Hua’s neck, after which all four of the men got into a car and drove off.
The Government also relied on the plea allocution of Li Wei to support the existence of a conspiracy to extort.12 In his plea hearing, Li Wei allocuted as follows:
Court: Did you commit the offense for which you have been charged?
Defendant: Yes.
Court: Please tell me in your own words what you did.
Defendant: On July 23rd, I went to 75 Eldridge Street with my co-defendant.
Court: July 23rd of what year?
Defendant: 2001.
Court: All right. And you went where, sir?
Defendant: 75 Eldridge Street.
Court: All right.
Defendant: To do the extortion that was on the indictment, to take money.
Court: To take money from whom?
*375Defendant: The owner of 75 [Eldridge Street],
Court: The owner of that building?
Defendant: Yes.
Court: Where is that address? Is that in Manhattan?
Defendant: Yes.
Court: And you agreed to do this with your co-defendant?
Defendant: Yes.
[Court]: Mr. Li, when you committed this act, you agreed with your co-defendant to do this extortion, as you say, did you agree to use force to . obtain this money?
Defendant: Yes.
Court: Or with the threat of force?
Defendant: Yes.
D. Analysis: Sufficiency of the Evidence
We are aware that “[c]ourts have interpreted the language [of] the Hobbs Act very broadly.” United States v. Arena, 894 F.Supp. 580, 587 (S.D.N.Y.1995). Nonetheless, we are bound by the fundamental principle that “the Due Process Clause protects the accused against conviction except upon proof beyond a reasonable doubt of every fact necessary to constitute the crime with which he is charged.” In re Winship, 397 U.S. at 364, 90 S.Ct. 1068. Here, it seems to us inescapable thai this standard has not been met.
The Indictment clearly and expressly charges Appellants with conspiring “to commit extortion, as the term is defined in [18 U.S.C. § 1951(b)(2) ], by conspiring to obtain property from and with the consent of others, ... which consent would be and was induced by the wrongful use of actual and threatened force, violence and fear.” The jury charge, too, expressly recited “the victim’s con[s]ent” as an element of extortion. There is nothing in the Record, however, to suggest that there was an agreement to obtain the property of either Hua or the gambling operation at 75- El-dridge by consent — forced or otherwise.' An inference may fairly be drawn that Appellants and others agreed to visit the 75 Eldridge Street parlor- to rob it, but that is all.
In particular, the evidence establishes that on at least eight separate occasions, Xiáo discussed an agreement between himself, Appellants, and others. But each time the criminal conduct was discussed, it was in terms of a robbery. Extortion was neither spoken of nor apparently ever contemplated. Indeed, not a single fact was elicited from Xiao that could lead to an inference that a co-conspirator planned, or agreed, to extort — as opposed to rob — the gambling parlor at 75 Eldridge Street or any individual at that location.
Again, absent from the Record is any indication that Appellants thought, or sought, to obtain property from Hua, or anyone else at 75 Eldridge Street, by means of a forced consent. Rather, the Record supports an agreement among, and an actual effort by, Appellants and others to get a person at that location to .open a door so that Appellants and others could enter the establishment and rob it. Indeed, this very method of robbery was discussed. But the only evidence that even arguably can be identified as indicating extortion came from Hua, who testified that he was gambling at the 75 Eldridge Street parlor when he received a phone call, either from Xiao or someone on Xiao’s behalf.
Hua testified that the caller demanded $10,000. Hua refused and hung up the phone. Later, Hua was summoned to *376come outside the parlor, where he was confronted by Xiao, Appellants, and another gangster, all of whom were pointing guns at Hua. Xiao demanded $10,000, and Hua refused, informing the gangsters that, he had no money. Xiao then hit Hua in the head, grabbing the chain from around his neck, and the gang fled. Xiao testified that the chain was later sold and that he, Appellant, and Li Wei then split the proceeds. It seems inescapable that this incident was nothing more nor less than a classic robbery.
Absent from Hua’s testimony is any suggestion that either Appellant was even involved in the alleged extortionate phone call. Hua’s testimony was inconsistent as to the identity of the caller, and he never identified either of the Appellants as the caller. The Government argues that Appellants must have been involved, because the call was placed after the gang formed up in Brooklyn and during the time that Xiao recalls traveling to 75 Eldridge. It is true that both the caller and the gang demanded $10,000, supporting the inference that it was one of the gangsters who placed the call. But even disregarding the uncertainty and vagueness of the timeline established by Xiao’s testimony and assuming arguendo that the gangsters made the call, absent from Hua’s testimony is any suggestion that the call itself conveyed any degree of threat — implied or express, violent or otherwise. Thus, either accepting Hua’s testimony alone, or-viewing it in conjunction with Xiao’s testimony (as the jury was instructed to do), the evidence does not support any inference of a threat in the phone call.
The Government contends,- however, that the fact of the phone call combined with the facts surrounding the gang’s visit to 75 Eldridge reasonably supports the inference that the purpose of the call was to extort, since the demand for $10,000, which was initially made by telephone, was then repeated by the gang in person before they resorted to violence and took the chain. Thus, concludes the Government, the phone call was both an attempted extortion and an act in furtherance of an extortion conspiracy. But again, there was no testimony that the call itself was threatening in any way. Nor was there any testimony from Xiao, or any other witness,-to fill this gap and place the call in a threatening and thus- extortionate context.
The caller recited no consequences — deleterious or otherwise — of a failure to tender the $10,000, and no evidence was put before the jury suggesting that any such consequences were implied by the caller or understood implicitly by Hua. Moreover, there was nothing in Hua’s testimony from which one could reasonably infer that he was placed in a subjective state of fear, or felt threatened in any way, by the call. Hua testified that Xiao “was somewhat familiar” to him; that he had seen Xiao “once or twice in Chinatown”; -and that he knew Xiao by the name “Vietnamese [B]oy.” But Hua said nothing from which a juror could reasonably infer that Xiao was feared in the neighborhood or known to be involved in criminal activities; nor was there anything else in the Record to support such an inference.13 Thus, the mere fact that the caller, whom Hua could not identify, stated that “Vietnamese Boy” would come to Hua’s gambling parlor to pick up the demanded $10,000 cannot support a rational inference that Hua was threatened or placed in fear by the caller. If the name “Vietnamese Boy” was intended to strike fear in the heart of Hua, there is simply no evidence that it in fact did so. *377Indeed, that Hua hung up the phone after stating simply that he had no money suggests that he saw no negative consequences in refusing to consent to the demand or, for that matter, in ignoring the call altogether.
It is notable that during Xiao’s testimony, he had ample opportunity to convey information indicating that he had agreed and planned with Appellants to extort Hua or the gambling business. But he never conveyed any such information. Rather, Xiao repeatedly described a robbery that was initiated and planned by him and Appellants. Indeed, as the gang arrived at 75 Eldridge and when they summoned Hua outside, their guns were already drawn and, thus, a robbery was then taking place. This was, therefore, not the culmination of an unsuccessful extortion or unfruitful extortion conspiracy but, rather, a full-fledged robbery under way.
A robbery plus a cryptic and ambiguous phone call does not equal extortion — at least, not on the facts presented to us in this case. And without some evidence in the Record to support the charges of extortion and conspiracy to extort, there was nothing to permit a rational jur'or to infer that what the defendants were about was anything other than a robbery and/or conspiracy to rob. Cf., e.g., Ceballos, 340 F.3d at 129-30.
Even considering the improperly admitted plea allocution of Li Wei, there simply was no evidence of an agreement to obtain property from Hua or anyone else with their consent through the threat or use of force, nor of any actual effort or attempt to do so. And, as discussed above, it is this notion that the victim of extortion consents to the taking — albeit through threat or force — that separates extortion from robbery. Indeed, in the Indictment, the Government charged Appellants with agreeing, intending, and attempting to take (Count One), and of taking (Count Two), with consent. But again, the Record contains no evidence that Appellants agreed, intended, or attempted to take with consent, by threat, the property of individuals associated with the gambling business at 75 Eldridge Street or that of the business itself, and Li Wei’s plea allocution does not cure this deficiency. Indeed, his statement that, on July 23rd, he “went to 75 Eldridge Street” with Appellants “[t]o do the extortion that was on the indictment, to take money” merely recites an ultimate legal conclusion without setting forth the requisite factual basis to support that conclusion.14
In light of all the foregoing, we conclude that thé evidence put forward by the Government to prove the charged extortion and conspiracy to extort, even viewed in the light most favorable to the prosecution, was insufficient as a matter of law to prove the crimes charged in Counts One and Two of the Indictment. At best, the evidence proves an uncharged conspiracy to rob, and the robbery of, an individual at 75 Eldridge Steet. Accordingly, we reverse the convictions of Appellants under Counts One and Two, for the crimes of conspiracy to extort and extortion, respectively.
E. Section 924-(c)
Appellants contend that the legal insufficiency of the evidence of the extor*378tion-related charges necessarily warrants reversal of the convictions of Appellants under the related firearm charge — for violation of 18 U.S.C. § 924(c)(1)(A) charged in Count Three. This statute creates a separate offense and provides a separate sentence for one who, “during and in relation to any crime of violence ... for which the person may be prosecuted in a court of the United States, uses or carries a firearm or who, in furtherance of any such crime, possesses a firearm.” Three elements comprise a § 924(c) violation: “First, the defendant must have used or carried a firearm.... Second, the government must prove the defendant used or carried a firearm knowingly---- [And third], the firearm must have been used or carried during and in relation to the underlying offense.” United States v. Dese-na, 287 F.3d 170, 180 (2d Cir.2002) (internal quotation marks omitted). At issue here is the meaning of the third element.
Appellants would have us rule that to satisfy that element, and as a prerequisite to a conviction under § 924, a defendant must be convicted of the predicate offense. While our Court has not previously had the opportunity to examine the question of what quantum of proof of a predicate offense must be established to sustain a related firearm conviction under 18 U.S.C. § 924(c)(1)(A), a number of our sister circuits have addressed this issue. And to sustain a § 924 conviction, those courts have invariably required that there be some legally cognizable quantum of proof of the predicate offense.15 See United States v. Lake, 150 F.3d 269, 275 (3d Cir.1998) (“In a prosecution under [section 924(c) ], the [Government must prove that the defendant committed a qualifying predicate offense .... ”); accord United States v. Jenkins, 90 F.3d 814, 821 (3d Cir.1996); see also Frye, 402 F.3d at 1128 (“‘[A] defendant charged with violating section 924(c)(1) must be proven to have committed the underlying crime ....’” (quoting Hunter, 887 F.2d at 1003)).16
While we do not, today, seek to map the farthest reaches of the statute, we think it consistent with both due process and the opinions of our sister circuits to hold that if the proof of the predicate crime is so fundamentally deficient that it could not sustain a conviction, then likewise, a conviction under § 924 cannot *379stand. Indeed, because the commission of the underlying predicate offense is a necessary element of a conviction under § 924(c), both logic and precedent dictate that there must be legally sufficient proof of the underlying offense. See, e.g., United States v. Macklin, 671 F.2d 60, 65 (2d Cir.1982) (“It is axiomatic that, in a criminal case, the [G]overnment must prove each and every element of the crime beyond a reasonable doubt.”); see also In Re Winship, 397 U.S. at 364, 90 S.Ct. 1068. Without such proof, the third element of § 924(c) simply has not been established, and a conviction under the statute cannot be sustained.
Here, since we conclude—in light of the quantum of evidence adduced in this case—that no rational jury could have convicted the Appellants of the charged extortion-related crimes, we also conclude that the convictions of Appellants under Count Three, for violating § 924 in connection with the extortion-related crimes, must be reversed as well.
II. Lin’s Mental Competence
A hearing to determine the mental competency of a criminal defendant “is required only if the court has ‘reasonable cause’ to believe that the defendant has a mental defect rendering him incompetent.” United States v. Nichols, 56 F.3d 403, 414 (2d Cir.1995) (quoting 18 U.S.C. § 4241(a)); see Pate v. Robinson, 383 U.S. 375, 385-86, 86 S.Ct. 836, 15 L.Ed.2d 815 (1966) (holding that due process may require a competency hearing to be held); see also Nicks v. United States, 955 F.2d 161, 168 (2d Cir.1992) (finding standards under § 4241 and due process essentially equivalent). “Because the necessity for a competency hearing varies in each case, depending upon a number of factors concerning defendant’s behavior and inferences which might be drawn from psychiatrists’ reports, the determination of whether there is reasonable cause to believe a defendant may be incompetent rests in the discretion of the district court.” Nichols, 56 F.3d at 414 (citations and internal quotation marks omitted); see also Drope v. Missouri, 420 U.S. 162, 180, 95 S.Ct. 896, 43 L.Ed.2d 103 (1975) (“There are, of course, no fixed or immutable signs which invariably indicate the need for further inquiry to determine fitness to proceed .... ”).
“In deciding that an evidentiary hearing is unnecessary, a court may rely not only on psychiatrists’ reports indicating competency but also on its own observations of the defendant.” Nichols, 56 F.3d at 414 (citations omitted). In United States v. Oliver, 626 F.2d 254 (2d Cir.1980), for example, this Court upheld the district court’s denial of a psychiatric examination and hearing “based solely on the judge’s direct observation and questioning of the defendant, despite evidence of the defendant’s low intelligence, prior history of-heavy drug use, lapses of memory, and unresponsiveness.” Nichols, 56 F.3d at 414 (citing Oliver, 626 F.2d at 258-59).
Here, Lin argues that the District Court abused its discretion in refusing to grant him a competency hearing after the Government revealed that there was cause to “question” the “credibility and accuracy” of the report submitted by Dr. Patenaude, the first prison psychologist to examine Lin. Lin further asserts that, in light of this revelation, he should have been examined by an “independent” psychologist— presumably, one mutually agreeable to Lin and the Government—rather than by another psychologist affiliated with, and selected by, the BOP, and that the court abused its discretion in refusing this request as well.
We disagree. That reasons came to light to question one prison psycholo*380gist’s findings does not compel the conclusion that the findings of any psychologist affiliated with the BOP would necessarily also be suspect. Indeed, quite the opposite: The fact that the BOP came forward proactively and apparently sua sponte with the information that led this Court to grant Lin the right to seek a second evaluation tends to prove that the Government was concerned with the veracity of the evaluation process, which in turn lends support to the District Court’s decision to rely on a second prison psychologist despite what had occurred previously. Moreover, it seems to us both reasonable and expeditious in this context to rely on the expertise of a forensic psychologist associated with the BOP, since psychologists working routinely in a penal setting are presumably familiar with patients similarly situated to Lin. It goes without saying, of course, that psychologists employed by the BOP, despite their affiliation with the Government, are bound by the same ethical and professional canons as their non-Government-affiliated colleagues. In any event, we see no abuse of discretion in the District Court’s selection of Dr. Rattan to evaluate Lin the second time.
We also reject Lin’s contention that he was entitled to a competency hearing. At bottom, Lin’s attorneys contend that because Lin consistently laughed in the face of the serious consequences of his actions and because he scored poorly on tests designed to measure his “problem-solving and reasoning” skills and had “difficulty with managing nonverbal information, perceiving visual data, organizing spatially oriented material, [and] mastering the abstract properties of visually presented symbols,” Lin probably was not competent to stand trial and be sentenced. Therefore, counsel contends, the District Court abused its discretion in failing to find “reasonable cause to believe that [Lin had] a mental defect rendering him incompetent.” Nichols, 56 F.3d at 414 (2d Cir.1995) (internal quotation marks omitted). We are unpersuaded.
We note that Dr. Rattan’s “principal working diagnosis” of Lin was “Adult Antisocial Behavior.” According to Dr. Rattan, this diagnosis was “considered less severe” than Lin’s previous (and now discredited) diagnosis of Antisocial Personality Disorder (or “APD”). Whereas the earlier diagnosis of APD was purportedly based on “a lifelong pattern of [Lin] relating to others in a maladaptive manner that [was] not thought subject to psychological treatment,” Dr. Rattan found “a lack of obtained evidence suggestive of ... behavioral disturbance prior to age [fifteen] ... and a lack of criteria met for APD on review of adult behavior.” Moreover, Dr. Rattan made the “[t]he diagnosis of Adult Antisocial Behavior ... per se on the basis of [Lin’s] conviction in this matter.” Finally, it is notable that Dr. Rattan found that the “lessening of diagnostic severity ... [was] seen as prognostic regarding [Lin’s] adjustment to an institutional setting.”
In any event, despite the noted findings, the bottom line of Dr. Rattan’s evaluation was that Lin “appeared competent for both trial and sentencing” (emphasis added). In particular, Dr. Rattan noted that Lin’s
performance on testing, although poor, was not consistent with function of those persons diagnosed with [mild mental retardation, or “Mild MR”]. Additionally, a review of [Lin’s] adaptive functions, required for a finding of Mild MR, suggests his “real world” function was probably in excess of formalized testing results. Specifically, [Lin’s] report of his illicit immigration, his use of “employment agencies,” his ability to speak some English despite his embeddedness in “China Town,” and frequent independent travel to “out of state” work sites *381is not consistent with the function of persons with Mild MR. His reliance on living with relatives in the United States is not culturally atypical, nor uncommon for relatively recent immigrants. Finally, a certain degree of deception was required for [Lin] during his. immigration and subsequent stay in the United States. Such “successful” deception, taken in context, is not likely consistent with the function of a person suffering from Mild MR.
Notably, Dr. Rattan also observed that Lin “was, and is, defensive, stubborn, and evasive regarding details of his case” and that, while these traits are “not considered a mental disease or defect,” they probably did “form the basis for [Lin’s] counsel’s concerns about [Lin’s] likely poor judgment and decision-making regarding his rejection of a plea offer in this matter.”
In light of Dr. Rattan’s evaluation as a whole, and mindful that the District Court observed Lin first-hand over a substantial period of time, we see no abuse of discretion on the part of the court in relying on Dr. Rattan’s findings, and on its own observations, in determining ultimately that there was no “reasonable cause,” 18 U.S.C. § 4241(a), to support the proposition that Lin “ha[d] a mental defect rendering him incompetent,” Nichols, 56 F.3d at 414.
III. Resentencing
The Government has conceded that a partial remand, pursuant to United States v. Crosby, 397 F.3d 103 (2d Cir.2005), is warranted.17 Where a criminal conviction is partly set aside, however, the typical course is simply to remand for resentencing. See, e.g., United States v. Boissoneault, 926 F.2d 230, 235 (2d Cir.1991); United States v. Swiderski, 548 F.2d 445, 452 (2d Cir.1977).18 In any event, “[t]his Court has power to do justice as the case requires.” Tinder v. United States, 345 U.S. 565, 570, 73 S.Ct. 911, 97 L.Ed. 1250 (1953); see 28 U.S.C. § 2106. In light of the District Judge’s reliance on the cumulative effect of Deal and in view of our reversal of the convictions of Appellants on Counts One, Two, and Three, we remand for resentencing on the remaining counts.
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In view of our disposition of these appeals, we decline to reach the arguments of Appellants concerning the admissibility of certain evidence under the Federal Rules of Evidence and/or Crawford v. Washington, 541 U.S. 36, 124 S.Ct. 1354, 158 L.Ed.2d 177 (2004). We have considered the parties’ remaining arguments and find them to be without merit..
CONCLUSION
For the foregoing reasons, the judgments are reversed insofar as they reflect the convictions of Appellants under Counts One, Two, and Three. The matters are remanded for entry of amended judgments dismissing those counts and for resentenc-ing by the District Court on the remaining counts.