OPINION
Defendant complains that a downward departure for cooperation with the government was improperly limited because she was given no notice in advance that the sentencing judge had doubts about her credibility. Because she failed to present any reason that the result would have been different had she challenged the judge’s impression, we will affirm the judgment.
Defendant pleaded guilty to one count of bank fraud in violation of 18 U.S.C. § 1344(1) and was sentenced to 24-months incarceration. Following the denial of her motion to reopen the sentencing record, defendant appealed. She contends that she was denied due process and advance notice of the sentencing judge’s intention to determine a fact adverse to her entitlement to a downward departure. See U.S.S.G. § 6A1.3.1
As part of her plea agreement, the defendant agreed to provide assistance to the government in the prosecution of her co-defendant, Jack Ogden. She testified against him at his trial, but the jury acquitted. Judge Lancaster presided over the two-day trial, as well as the defendant’s sentencing which occurred two weeks later. Following the Ogden trial, the government filed a § 5K1.1 motion for a downward departure stating that “[Carey] gave truthful responses to all questions put to her and has otherwise cooperated fully and completely within the meaning of her plea agreement and § 5K1.1....”
The Guideline calculation yielded a range of 30-37 months’ incarceration. Af*390ter counsel’s argument at the sentencing hearing, Judge Lancaster commented on the defendant’s extensive criminal history, filled as it was “with theft and fraud offenses so great that she is in the same category as career offenders for sentencing purposes.” He noted that he had intended “to give the maximum penalty of 37 months.”
The judge did, however, agree to consider the government’s motion for a sentence reduction for the defendant’s assistance during the Ogden trial. In determining the downward departure, the judge noted that he was taking the accuracy of her testimony in the Ogden case into account. “In all candor in my view I do not believe she was truthful during the testimony. I believe she embellished the criminality of her co-defendant in order to get this downward departure. She attributed conduct to him even the government didn’t....” After allowing a 10-month credit for pretrial incarceration, the judge granted an additional three month reduction pursuant to the § 5K1.1 motion.
Defense counsel then asked the court to reconsider the sentence based on the defendant’s good behavior during the preceding year. The judge responded, “I have given thought to the sentence. I don’t do this lightly. I understand what I am doing. I understand two years in the federal penitentiary is rough. I think she needs to be in a structured environment for a while.”
Following the sentencing hearing, the defendant moved to reopen the record, asserting that the court’s failure to put her on notice that the truthfulness of her testimony was a disputed sentencing factor foreclosed her opportunity to respond. The District Court denied the motion, noting that it had granted a departure that took “into consideration, among other things, the defendant’s own testimony. Defendant should not be surprised or feel ambushed because the court undertook the evaluation required by § 5K1.1.”
On appeal, defendant cites Sentencing Guideline § 6A1.3, which states that a court should not rely on a factor important to a sentencing determination without first alerting the parties that the factor is in dispute and granting the right to challenge any adverse finding. She also claims that this lack of notice denied her Due Process under the Fifth Amendment.
I.
Generally speaking, we do not have jurisdiction to hear a defendant’s claim that a downward departure was inadequate. United States v. Minutoli, 374 F.3d 236 (3d Cir.2004) (no jurisdiction “where a District Court allegedly made a mistake of fact when, in the exercise of its discretion, it refused” to depart downward); United States v. Khalil, 132 F.3d 897 (3d Cir.1997) (no jurisdiction where there has been some exercise of the court’s discretion in departing downward); United States v. Denardi, 892 F.2d 269 (3d Cir.1989)(same).2 However, in this case, the defendant alleges a violation of the Constitution, a rule of criminal procedure, as well as an incorrect application of a Guideline. 18 U.S.C. §§ 3742(a)(1) and (2) permit appeal of a sentence if it was imposed in violation of law [or] was imposed as a result of an incorrect application of the Sentencing Guidelines. See United States v. Ruiz, 536 U.S. 622, 122 S.Ct. 2450, 153 L.Ed.2d 586 (2002).
Whether a sentencing factor is a permissible basis for departure is a ques*391tion of law. Accordingly, we have jurisdiction to entertain this appeal. We exercise plenary review over the District Court’s interpretation and application of the Guidelines. United States v. Figueroa, 105 F.3d 874, 875-6 (3d Cir.1997). Under the PROTECT ACT’s amendments to 18 U.S.C. 3742(e), which are applicable to this case, see United States v. Dickerson, 381 F.3d 251 (3d Cir.2004), we are required to “give due regard to the opportunity of the district court to judge the credibility of the witnesses.”
II.
It may be helpful to review the procedures applicable to a downward departure based upon the defendant’s cooperation with the government. First, the sentencing court may lower the period of incarceration only after a motion by the prosecutor under 18 U.S.C. § 3553(c). See United States v. Bruno, 897 F.2d 691 (3d Cir.1990).
Once the government has filed an appropriate motion, the authority returns to the district court. “It is the District Court’s decision, not the prosecutor’s, whether to depart and to what extent ... [T]he government’s filing of a § 5K1.1 motion ‘does not bind a sentencing court to abdicate its responsibility [or] stifle its independent judgment.’ ” United States v. Casiano, 113 F.3d 420 (3d Cir.1997) (citing United States v. Mariano, 983 F.2d 1150, 1155 (1st Cir.1993)). As one court phrased it, “[t]he District Court is not obligated to depart downward simply because a grateful prosecutor prefers a lighter sentence.” Mariano, 983 F.2d at 1155. A prosecutor’s opinion of the defendant’s truthfulness stated in a § 5K1.1 motion is understandably affected by an advocate’s bias and does not foreclose a contrary appraisal by a neutral, impartial judge.
Nevertheless, once the district court decides to grant a § 5K1.1 motion, “there are some parameters to the exercise of the court’s discretion.” Although “the bases for substantial assistance departures listed in § 5K1.1 are not meant to be exhaustive, they are instructive.” Casiano, 113 F.3d at 429. According to the Guideline, “(a) the appropriate reduction shall be determined by the court for reasons stated that may include, but are not limited to, consideration of the following:
(1) the Court’s evaluation of the significance and usefulness of a defendant’s assistance taking into consideration the government’s evaluation of the assistance rendered;
(2) the truthfulness, competent completeness and reliability of any information or testimony provided by the defendant.” [3] U.S.S.G. § 5Kl.l(a). As we said in United States v. King, 53 F.3d 589, 591 (3d Cir.1995), a proper exercise of the District Court’s discretion under 5K1.1 “involves an individualized qualitative examination of the incidents of the defendant’s cooperation .... ”
On occasion, and despite the terms of a government recommendation, factors other than those listed in 5K1.1 have been considered in deciding the extent of a departure. Casiano, 113 F.3d at 430 (nature and circumstances of the offense may be taken into account in limiting the extent of a § 5K1.1 reduction); United States v. Webster, 54 F.3d 1, 4 (1st Cir.1995) (limiting extent of § 5K1.1 departure so as not to “offset” the impact of a mandatory 60-day month consecutive sentence); United States v. Alvarez, 51 F.3d 36, 39-40, 41 n. 5 (5th Cir.1995) (limiting departure to avoid disparity in sentences with less culpable coconspirators); United States v. Carnes, 945 F.2d 1013, 1014 (8th Cir.1991) (limiting departure in light of prosecutor’s failure to press weapon charges).
*392The court’s reservations here as to the extent of the defendant’s truthfulness were within the factors cited in the Guidelines and are not subject to attack as being an impermissible criterion. In sum, a District Court has authority to refuse or grant a downward departure under § 5K1.1 and is granted broad discretion in determining the extent of the reduction.
III.
We now turn to the defendant’s objection that she was entitled to notice that the departure would be affected by the court’s doubts as to the truthfulness of her testimony at the Ogden trial.
The Sentencing Guidelines require the court to provide the parties with .an adequate opportunity to present information when a sentencing factor is reasonably in dispute. See U.S.S.G. § 6A1.3(a). In Burns v. United States, 501 U.S. 129, 111 S.Ct. 2182, 115 L.Ed.2d 123 (1991), the Supreme Court held that Fed. R. Crim. P. 32 requires “reasonable notice” to parties before a district court considers an upward departure on a ground not identified in the pre-sentence report or in a pre-hearing submission.
Fed.R.Crim.P. 32(h) was amended in 2002 to read somewhat more expansively than the holding in Bums. The Rule currently reads, “[bjefore the Court may depart from the applicable sentencing range on a ground not identified for departure either in the pre-sentence report or in a party’s pre-hearing submission, the court must give the parties reasonable notice that it is contemplating such a departure. The notice must specify any ground on which the court is contemplating a departure.” Taken together, the Guidelines, Rules of Criminal Procedure and case law provide that, in general, when there are factors that may have a measurable effect on the applicable punishment, notice must be given to the defendant to allow an opportunity to comment on their accuracy.
Failure to give notice which realistically prevents a defendant from presenting evidence on a disputed point may, in some circumstances, affect substantial rights and require re-sentencing. See United States v. Himler, 355 F.3d 735 (3d Cir.2004). However, in United States v. Reynoso, 254 F.3d 467, 475 (3d Cir.2001), the court concluded that although Fed. R.Crim.P. 32 had been violated, the error was harmless because even if notice had been given there was nothing that defense counsel would have done differently at the sentencing hearing.
Similarly, United States v. Nappi, 243 F.3d 758, 770 (3d Cir.2001), determined that failure to provide notice was not plain error unless the defendant would have done something by way of argument or proof that probably would have affected the outcome. See also United States v. Rivera, 192 F.3d 81 (2d Cir.1999).
There is a paucity of cases citing a lack of notice to challenge a limited downward adjustment; in most cases citing lack of notice, the issue was a “surprise” upward adjustment or failure to grant any downward departure whatsoever. In United States v. Patrick, 988 F.2d 641, 648 (6th Cir.1993), the sentencing judge relied on the testimony and bearing of a co-defendant at his plea hearing to justify a sentence enhancement for defendant Patrick because of his leadership role. The Court of Appeals concluded that advance comment on the co-defendant’s testimony would not have provided Patrick with any additional incentive or ability to challenge its accuracy. “To the extent that the sentencing judge relied on a comparison of the demeanors of the two defendants, that evidence was essentially irrebuttable.” Had the sentencing judge earlier notified *393Patrick that his “bearing, as compared to that of his co-defendant, was that of a leader, it is difficult to see what evidence or arguments such a disclosure would have prompted Patrick to offer.” Patrick, 988 F.2d at 648.
By comparison, in United States v. Himler, the sentencing court based an upward departure on the economic impact on the victims caused by the defendant’s conduct, and did so sua sponte and without any notice to the parties. On appeal, Himler asserted that if a warning had been given, he would have subpoenaed certain financial records bearing on the financial security of the victims, investigated factors underlying the sale of property which had a connection with the charged fraud, as well as invoked Guidelines provisions that disfavored enhancement in the circumstances. Based on the assertion that such specific measures would have been employed had notice been given, we concluded that re-sentencing was required. Himler, 355 F.3d at 743. It is worth noting that the specific avenues of defense foreclosed by lack of notice in that case were quite different from the circumstances in Patrick.
IV.
Fed.R.Crim.P. 32(h) speaks to a “departure from the applicable sentencing range” when no notice was given either in the pre-sentence report or a submission by a party. In this case notice was given through the government’s motion under 5K1.1 for a reduction of sentence and therefore, by its terms, the Rule does not apply.
Moreover, Rule 32(h) does not limit a court’s discretion as to the extent of a downward departure it may apply. See United States v. King, 53 F.3d at 591 (noting that the extent of a departure is a “non-mechanical process,” by which a sentencing court must give “appropriate weight to the government’s assessment and recommendation, [but still] consider all other factors relevant to this inquiry.”)
Accordingly, we conclude that the defendant is not entitled to any relief under Rule 32(h).
Finally, we consider the defendant’s challenge to the lack of notice under Sentencing Guideline § 6A1.3.
Nothing in the Guideline purports to require the sentencing judge to disclose in advance such matters as his appraisal of the undisputed material contained in the pre-sentence report, impressions created by the defendant’s conduct during a trial, or the nature of the violation. Indeed, such announcement of the judge’s tentative feeling about factors bearing on appropriate punishment might undermine the efficacy of the sentencing hearing. An unwillingness to change one’s publicly declared opinion is not a stranger to the judiciary.
Moreover, a remand for re-sentencing should not be required unless there is reason to believe that an injustice has occurred that can be corrected by reconsideration. We are not persuaded that that has occurred in this case.
This case is unlike those where a sentencing judge relied on testimony of a co-defendant in another proceeding as the basis for a sua sponte enhancement. See, e.g., United States v. Berzon, 941 F.2d 8 (1st Cir.1991). Here it was the testimony of the defendant herself that was under scrutiny. Defendant was fully aware of what she had said as a witness. The same judge who heard all of the testimony in the Ogden trial was in a unique position to make a judgment on the defendant’s truthfulness as required by § 5K1.1. In such circumstances, the likelihood of effective rebuttal is extremely slim.
To some extent the judge’s evaluation of her veracity is similar to the im*394pressions gathered by the sentencing judge in the Patrick case. We need not term the appraisal here as “irrebuttable,” but we would expect defendant to point to specific steps she could have taken to change the judge’s conclusion on what he had seen and heard in the Ogden trial. Only two weeks elapsed between the trial and the sentencing so the facts were still fresh in the minds of both defendant and her counsel who had been in the courtroom during her testimony.
Defendant did not immediately object to the sentencing judge’s reaction to her testimony, but did so in her motion to reconsider. However, neither in that motion nor in the briefs in this appeal did she state what steps she would have taken to alter the sentencing judge’s opinion. If the defendant does not point to a deprivation that could affect the outcome, re-sentencing is not required. Thus, this case fails the test set out in Hinder,3
Moreover, the sentencing decision was obviously influenced by the defendant’s extensive criminal record which began in 1980. As the judge remarked, “short incarcerations have done little to dissuade her from her criminal life ... I think she needs to be in a confined environment ... I think 24 months confined under strict supervision is necessary for this woman.” These comments further indicate that advance notice of the judge’s skepticism about the defendant’s truthfulness at the Ogden trial would likely not have affected the ultimate sentence imposed.
Accordingly, the judgment of the District Court will be affirmed.