ORDER DENYING CERTIFICATE OF APPEALABILITY*
Defendant Alfonso Moya-Breton filed a motion for relief under 28 U.S.C. § 2255 in the United States District Court for the District of Utah, claiming that he had received ineffective assistance of trial and appellate counsel. The court denied the motion and Defendant’s request for a certificate of appealability (COA) to appeal the denial. See 28 U.S.C. § 2253(c)(1)(B) (requiring COA to appeal denial of relief under § 2255). Defendant now seeks a COA from this court. Because he fails to make “a substantial showing of the denial of a constitutional right,” id. § 2253(c)(2), we deny his application for a COA and dismiss this appeal.
I. BACKGROUND
A. Factual Background
Defendant’s conviction on drug and firearm charges was affirmed on direct appeal. See United States v. Moya-Breton, 329 Fed.Appx. 839 (10th Cir.2009). The issues before us relate only to Defendant’s alleged interactions with his trial counsel. In an affidavit submitted with his § 2255 motion, he asserts the following: He met with his trial counsel four times before trial. On the first visit, counsel discovered that Defendant did not speak English. Counsel returned for a second visit with a Spanish translator. During that visit, counsel informed Defendant that the government did not have much evidence against him. On the third visit, counsel reiterated that the government had little evidence implicating Defendant. When Defendant asked counsel if the government would release him, counsel explained that unless the government dismissed the charges, which was unlikely, Defendant would have to proceed to trial and be found innocent. Counsel further explained that if Defendant was found guilty at trial, he would face a maximum penalty of 17 years in prison. Upon hearing this infor*713mation, Defendant asked counsel to negotiate a “fair plea” because “proceeding to trial seemed risky.” R., Vol. 1 at 72. Counsel stated that he would speak with the government about a “reasonable plea offer.” Id. On the final pretrial visit, Defendant immediately asked counsel about a plea bargain. Counsel responded that the government had not returned his calls. Defendant asked counsel to attempt to “obtain a plea for (10) years, or anything close to that[,]” id., and counsel said that he would try. Defendant told counsel “to just get me a good plea bargain, because I don’t want to proceed to trial unless I just have no other choice.” Id. (internal quotation marks omitted). Counsel reiterated that the government had little evidence against Defendant and that Defendant would face a maximum sentence of 17 years. Defendant next met with counsel on the first day of trial, when he asked counsel about any potential plea offers. Counsel responded that “apparently the government is not interested in making a plea deal, because they did not return [my] phone calls.” Id. at 73 (internal quotation marks omitted).
The jury convicted Defendant on multiple counts, and he was sentenced to 360 months’ imprisonment. According to Defendant’s affidavit, after the district court pronounced sentence he turned to his trial counsel and asked about the alleged maximum sentence of 17 years, but counsel said that he did not know what had happened.
B. Procedural History
On appeal Defendant’s sole issue was prosecutorial misconduct during closing argument. See Moya-Breton, 329 Fed.Appx. at 841. We affirmed, and the Supreme Court denied Defendant’s petition for a writ of certiorari on October 5, 2009. See Moya-Breton [sic] v. United States, — U.S. -, 130 S.Ct. 279, 175 L.Ed.2d 187 (2009).
On August 13, 2010, Defendant filed his § 2255 motion. The motion and supporting brief raised four claims of ineffective assistance of counsel: (1) that trial counsel “fail[ed] to negotiate, secure, and/or disclose a plea offer with the government where the evidence demonstrated overwhelming guilt,” R., Vol. 1 at 48 (full capitalization omitted); (2) that trial counsel “grossly misadvised [him] of applicable laws, statutes, and potential sentencing exposure,” id. at 51 (full capitalization omitted); (3) that trial and appellate counsel “fail[ed] to object [to] an ... inapplicable weapon enhancement,” id. at 54 (full capitalization omitted); and (4) that trial and appellate counsel “fail[ed] to investigate, discover, and exploit false testimony given by the government’s primary witness during trial,” id. at 56 (full capitalization omitted). The motion also requested an evidentiary hearing. Along with the § 2255 motion, Defendant moved for discovery of communications between the government and his attorney and of records relating to the government’s principal witness at trial. It does not appear that the district court ever ruled on the motion.
On March 30, 2011, the district court denied Defendant’s § 2255 motion on the merits. On June 30 Defendant moved the court to reconsider its denial. But it denied the motion for lack of jurisdiction because Defendant had already appealed.
II. DISCUSSION
Reading liberally Defendant’s application for a COA, see Erickson v. Pardus, 551 U.S. 89, 94, 127 S.Ct. 2197, 167 L.Ed.2d 1081 (2007), Defendant appears to challenge the district court’s ruling on the following grounds: (1) that he was denied effective assistance of trial counsel (he appears to have abandoned his claims of *714ineffectiveness of appellate counsel); and (2) that the court violated his right to due process by not ruling on his discovery motions, his request for an evidentiary hearing, and his request for appointed counsel to represent him.
“A certifícate of appealability may issue ... only if the applicant has made a substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2). “Where a district court has rejected the constitutional claims on the merits,” the prisoner “must demonstrate that reasonable jurists would find the district court’s assessment of the constitutional claims debatable or wrong.” Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000). We recognize that in determining whether to issue a COA, a “full consideration of the factual or legal bases adduced in support of the claims” is not required. Miller-El v. Cockrell, 537 U.S. 322, 336, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003). Instead, the decision must be based on “an overview of the claims in the habeas petition and a general assessment of the merits.” Id.
A. Ineffective Assistance of Counsel
Defendant alleges three instances of ineffective assistance of counsel. First, he contends that his counsel failed to inform him that the government had extended a plea offer, and that this failure denied him his right to choose whether to accept or reject the offer. Second, he contends that his counsel failed to advise him properly on how to plead. Third, he claims that counsel did not know the law applicable to his case and provided inaccurate information regarding his potential sentencing exposure.
To establish that counsel was ineffective, Defendant must show both “that counsel’s representation fell below an objective standard of reasonableness” and that he was prejudiced by the deficient performance. Strickland v. Washington, 466 U.S. 668, 687-88, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Our review of counsel’s performance is “highly deferential,” to avoid the distortion of hindsight; and we presume that counsel was effective unless the defendant shows otherwise. Id. at 689-90, 104 S.Ct. 2052. Because reasonable jurists would not find the district court’s denial of Defendant’s ineffective-assistance claims debatable or wrong, we deny his request for a COA on these claims.
1. Failure to Communicate a Plea Offer
Although defense counsel has a duty to convey plea offers to the client, Defendant failed to allege any facts that would support his speculation that his trial counsel violated that duty. As the district court noted in its decision, Defendant’s § 2255 motion conceded that he did not know whether the government had made any plea offers to his counsel and that his counsel had told him that the government had not returned his calls regarding a plea bargain. Thus, this claim clearly fails on the first prong of the Strickland test— defective representation.1 We also doubt *715that Defendant made adequate allegations that he would have accepted a plea offer from the government (and thus suffered prejudice from the failure to convey an offer); but we need not resolve that issue.
2. Failure to Advise of Right to “Open Plea”
Defendant argues that his counsel was ineffective in failing to advise him that he could have entered an open plea without a plea agreement. But this argument was not made in district court, and the district court did not consider it. The phrase “open plea” does not appear in Defendant’s § 2255 motion or in the supporting brief, nor does any other articulation of the issue. Although the issue is raised in his district-court traverse, such a pleading, like a reply brief, is not a proper vehicle to raise a new issue. See Jackson v. Duckworth, 112 F.3d 878, 880 (7th Cir.1997); see also United States v. Harrell, 642 F.3d 907, 918 (10th Cir.2011) (“[Arguments raised for the first time in a reply brief are generally deemed waived.”). Accordingly, we will not address the issue. See Coppage v. McKune, 534 F.3d 1279, 1282 (10th Cir.2008).
3. Counsel’s Lack of Knowledge Regarding Applicable Law and Failure to Advise of Sentencing Exposure
Defendant argues that his counsel did not have sufficient knowledge of the law applicable to his case and failed to advise him properly regarding the potential prison sentence he would face should he proceed to trial. In rejecting this argument, the district court said that the record did not support the contention that Defendant was not advised of the potential penalty for his crimes. The court also concluded that even if trial counsel had given Defendant wrong information, he had not suffered any prejudice. At the least, Defendant must show that he would have acted differently if his counsel’s advice had been proper. But his brief in this court does not assert that he would have acted differently except by arguing that he may have decided to plead guilty even without a plea agreement. As previously discussed, however, Defendant did not properly raise that argument in district court. Therefore, no reasonable jurist could debate that the district court erred in dismissing this claim for failure to allege prejudice.
B. Motion for Discovery
Defendant argues that the district court violated his right to due process by not ruling on his discovery motions. But he was not entitled to discovery. Under Rule 6(a) of the Rules Governing Section 2255 Proceedings for the United States District Courts, “[a] judge may, for good cause, authorize a party to conduct discovery under the Federal Rules of Criminal Procedure or Civil Procedure, or in accordance with the practices and principles of law.” In the context of a proceeding under 28 U.S.C. § 2254, we have held that “[g]ood cause is established ‘where specific allegations before the court show reason to believe that the petitioner may, if the facts are fully developed, be able to demonstrate *716that he is entitled to relief.’ ” Wallace v. Ward, 191 F.3d 1235, 1245 (10th Cir.1999) (quoting Bracy v. Gramley, 520 U.S. 899, 908-09, 117 S.Ct. 1793, 138 L.Ed.2d 97 (1997)) (ellipses omitted), modified on other grounds, McGregor v. Gibson, 248 F.3d 946, 953 (10th Cir.2001) (en banc). We see no reason to apply a different standard here.
In his discovery motion Defendant baldly asserted that discovery was required “to adequately obtain the evidence necessary to prove petitioner’s claims of ineffective assistance of counsel; suborned perjury; falsification of government evidence, and intentional neglect.” R., Vol. 1 at 76. He failed, however, to provide specific allegations showing reason to believe that the requested discovery would produce information supporting his ineffectiveness claims. Therefore, neither the federal rules nor the fundamental fairness required by due process entitled him to discovery. The district court did not abuse its discretion in denying Defendant’s request for discovery. See Wallace, 191 F.3d at 1245-46.
C. Evidentiary Hearing
Defendant asserts that the district court violated his right to due process by not ruling on his request for an evidentiary hearing. “We review the denial of an evidentiary hearing in a § 2255 proceeding for an abuse of discretion.... ” United States v. Clingman, 288 F.3d 1183, 1187 n. 4 (10th Cir.2002). Because “there were no relevant, disputed issues of fact that needed to be resolved,” we deny Defendant’s request for a COA on this issue. United States v. Gonzalez, 596 F.3d 1228, 1244 (10th Cir.2010).
D. Appointment of Counsel
Finally, Defendant argues that the district court violated his right to due process by not appointing counsel to represent him. But, as Defendant concedes, he has no constitutional right to counsel in a habeas proceeding. Except when “the district court determines that an evidentiary hearing is required,” “[t]he decision to appoint counsel is left to the sound discretion of the district court.” Engberg v. Wyoming, 265 F.3d 1109, 1122 & n. 10 (10th Cir.2001) (internal quotation marks omitted); cf. Rule 8(c) of the Rules Governing Section 2255 Proceedings for the United States District Courts (“If an evidentiary hearing is warranted, the judge must appoint an attorney to represent a moving party who qualifies to have counsel appointed under 18 U.S.C. § 3006A.”). Because Defendant has not shown that the district court abused its discretion, we deny his request for a COA on this claim.
III. CONCLUSION
We DENY Defendant’s application for a COA and dismiss this appeal.