
549 F.3d 921 (2008)
UNITED STATES of America
v.
John D. CORSO, III, Appellant.
No. 07-3901.
United States Court of Appeals, Third Circuit.
Argued October 1, 2008.
Filed: December 15, 2008.
*923 Candace Cain (Argued), Office of Federal Public Defender, Pittsburgh, PA, Attorney for Appellant.
Robert L. Eberhardt, Laura S. Irwin (Argued), Kelly R. Labby, Office of United States Attorney, Pittsburgh, PA, Attorneys for Appellee.
Before: FISHER, CHAGARES and HARDIMAN, Circuit Judges.

OPINION OF THE COURT
FISHER, Circuit Judge.
Pursuant to a written plea agreement, John D. Corso, III pleaded guilty to one count of theft of mail, in violation of 18 U.S.C. § 1708. The District Court sentenced him to twenty-one months of imprisonment and two years of supervised release. Corso appeals from the District Court's judgment of sentence, arguing that the District Court committed numerous procedural errors in imposing his sentence and that his sentence is substantively unreasonable. Because we conclude that Corso validly waived the right to appeal his sentence, we will affirm.

I.

A.
John Corso worked as a driver for T. Wilson Trucking, a private company that contracted with the United States Postal Service to transport mail along certain "highway contract routes" between Postal Service facilities in Pennsylvania, In January 2005, postal inspectors determined *924 that rifled mail found in a collection box in Aliquippa had come from sources along a contract route handled by Corso. In response, the inspectors placed a "test letter" containing cash in a bundle of first-class mail to be transported by Corso to a processing and distribution center in Pittsburgh.
The inspectors covertly watched Corso collect the bundle containing the test letter, but by the time he unloaded his cargo in Pittsburgh the test letter was missing. After stopping Corso before he could leave the distribution center, the inspectors found the test letter, as well as four other stolen letters, in the cab of his truck. When confronted, Corso first denied any wrongdoing, but eventually admitted that he had stolen mail on three or four occasions and that he had taken between five and twenty-five pieces of mail each time.

B.

1.
On November 8, 2006, an indictment was returned in the Western District of Pennsylvania charging Corso with five counts of theft of mail in violation of 18 U.S.C. § 1708, one count for each of the letters found in the cab of his truck. After initially pleading not guilty, Corso eventually entered into a plea agreement with the government. In the agreement, Corso agreed to plead guilty to Count One of the indictment, acknowledged his responsibility for the conduct charged in the remaining four counts, and stipulated that the District Court could consider the conduct charged in those four counts in imposing sentence. In exchange for Corso's guilty plea, the government agreed to move to dismiss the remaining four counts against him and to recommend a two-level reduction in offense level for acceptance of responsibility under § 3E1.1 of the United States Sentencing Guidelines. The parties made a non-binding stipulation that the total loss resulting from the offense was $300.00 and agreed that Corso faced a maximum term of imprisonment of five years and a maximum term of supervised release of three years.
The plea agreement also contained an appellate-waiver provision, which read as follows:
"8. John D. Corso, III waives the right to take a direct appeal from his conviction or sentence under 28 U.S.C. § 1291 or 18 U.S.C. § 3742, subject to the following exceptions:
(a) If the United States appeals from the sentence, John D. Corso, III may take a direct appeal from the sentence.
(b) If (1) the sentence exceeds the applicable statutory limits set forth in the United States Code, or (2) the sentence unreasonably exceeds the guideline range determined by the Court under the Sentencing Guidelines, John D. Corso, III may take a direct appeal from the sentence.
John D. Corso, III further waives the right to file a motion to vacate sentence, under 28 U.S.C. § 2255, attacking his conviction or sentence, and the right to file any collateral proceeding attacking his conviction or sentence."
Corso and his attorney signed the plea agreement. By signing, Corso acknowledged that he had read the agreement, had discussed it with his attorney, and had accepted it.

2.
On June 1, 2007, the District Court held a change-of-plea hearing, during which it engaged Corso in a colloquy intended to ensure that he was knowingly and voluntarily entering his guilty plea and that he *925 understood the contents of his plea agreement, as required by Federal Rule of Criminal Procedure 11(b). After placing Corso under oath, the District Court reviewed with him the rights incident to pleading not guilty and assured itself that Corso understood that, by changing his plea to guilty, he was giving up those rights. The District Court also confirmed that Corso was satisfied with the legal representation he had received, that he had not been threatened or otherwise coerced into pleading guilty, and that he understood the charges against him, the maximum penalties that could be imposed, and that the District Court was "not obligated to sentence [him] within the guideline range" because the Sentencing Guidelines "are not mandatory on [the court]."
At the District Court's request, the prosecutor "outlined" the substance of the plea agreement. But the prosecutor made only one brief allusion to the agreement's appellate-waiver provision, mentioning that the agreement contained "the standard language regarding waiver of appeal in that it sets forth the only exceptions to it." The District Court declined to expand on the prosecutor's synopsis, and at no point in the colloquy did it explain to Corso the implications of the appellate-waiver provision or inquire if he understood that he was waiving his right to appeal.
Following the colloquy, Corso pleaded guilty to one count of mail fraud. The District Court accepted Corso's guilty plea, finding that Corso was competent and capable of entering an informed plea and that he was knowingly and voluntarily pleading guilty.

3.
After the District Court accepted Corso's guilty plea, the United States Probation Office prepared a presentence report (PSR) using the November 2006 Sentencing Guidelines. Beginning with a base offense level of 6 under Guidelines § 2B1.1, the Probation Office recommended a four-level enhancement under § 2B1.1(b)(2)(B) for an offense involving between 50 and 250 victims, a two-level enhancement under § 3B1.3 for abuse of a position of trust, and a two-level reduction under § 3E1.1 for acceptance of responsibility. The resulting total offense level of 10, combined with Corso's criminal history category of V, yielded an advisory Guidelines range of twenty-one to twenty-seven months of imprisonment.
On September 7, 2007, the District Court held a sentencing hearing, at which Corso objected to both of the PSR's recommended sentencing enhancements. Corso objected to the number-of-victims enhancement on the grounds that his offense did not involve fifty or more victims (because the stipulated total loss was $300) and that the Probation Office erroneously relied on the "special rule" described in Application Note 4(C)(ii)(I) to § 2B1.1 to justify presuming the contrary.[1] The special rule was inapplicable, Corso argued, because the delivery truck involved in his offense belonged to T. Wilson Trucking, not the United States Postal Service, and thus was not a "Postal Service delivery vehicle" within the meaning of the application note. Corso objected to the abuse-of-trust enhancement on a similar ground, arguing that he was an employee of a private trucking company, not of the Postal Service, and, as such, was not in a *926 position of trust as contemplated by § 3B1.3.
The District Court rejected Corso's arguments and, again emphasizing that it understood that the Guidelines were advisory in nature, accepted the PSR's recommendations, including the proposed enhancements and Guidelines range. After reviewing the sentencing factors set forth in 18 U.S.C. § 3553(a) and hearing the parties' arguments, the District Court sentenced Corso to twenty-one months of imprisonment and two years of supervised release. It explained that Corso's "personal circumstances" were "simply not different enough to warrant a sentence different from that recommended by the guidelines" and that, "[i]n the Court's view, the sentence will adequately address the sentenc[ing] goals of punishment, rehabilitation and deterrence." It then told Corso the following:
"Sir, you have a right to appeal this sentence. If you want to appeal this sentence, you must do so within ten days. If you cannot afford the costs of appeal, you may apply for leave to appeal in forma pauperis. If you cannot afford an attorney, I'll appoint one to represent you free of charge. Do you understand what your appeal rights are?"
Corso responded in the affirmative, and the government did not object to, or otherwise attempt to correct, the District Court's statement.
Corso filed a timely notice of appeal, challenging his sentence. On appeal, Corso argues that the District Court committed procedural error by (1) erroneously applying the number-of-victims and abuse-of-trust enhancements in calculating his Guidelines range, (2) treating the Guidelines as mandatory, and (3) failing to adequately consider the § 3553(a) sentencing factors. He also contends that his sentence is substantively unreasonable in light of the § 3553(a) factors.
The government argues that Corso's appeal is barred by the appellate-waiver provision contained in his plea agreement. Corso responds that the waiver is inapplicable to this appeal because his grounds for appeal fall within one of the waiver's exceptions. He also maintains that he did not knowingly and voluntarily agree to the waiver because the District Court failed during the colloquy at the change-of-plea hearing to adequately inform him of the waiver's terms and to ensure his understanding of those terms, as required by Federal Rule of Criminal Procedure 11(b)(1)(N).

II.
The District Court had subject matter jurisdiction under 18 U.S.C. § 3231. We have jurisdiction under 28 U.S.C. § 1291 and 18 U.S.C. § 3742(a). See United States v. Gwinnett, 483 F.3d 200, 203 (3d Cir.2007). Where, as here, the government invokes an appellate-waiver provision contained in a defendant's plea agreement, we must determine as a threshold matter whether the appellate waiver prevents us from exercising our jurisdiction to review the merits of the defendant's appeal. See United States v. Goodson, 544 F.3d 529, 533-37 (3d Cir. 2008) (holding that an appellate waiver "has no bearing on an appeal if the government does not invoke its terms"); Gwinnett, 483 F.3d at 203 ("[T]his court retains subject matter jurisdiction over the appeal by a defendant who had signed an appellate waiver.").
Generally, our review of the validity and scope of appellate waivers is plenary. United States v. Jackson, 523 F.3d 234, 237 (3d Cir.2008); see also Goodson, 544 F.3d at 537 n. 6. But when a defendant *927 seeks to set aside his appellate waiver based on an unpreserved claim that the district court did not conduct an adequate colloquy under Federal Rule of Criminal Procedure 11(b)(1)(N), we review the alleged Rule 11 violation for plain error. Goodson, 544 F.3d at 539 & n. 9 (interpreting United States v. Vonn, 535 U.S. 55, 122 S.Ct. 1043, 152 L.Ed.2d 90 (2002)).

III.

A.
We will decline to exercise our jurisdiction to review the merits of Corso's appeal if we conclude (1) that the issues he pursues on appeal fall within the scope of his appellate waiver and (2) that he knowingly and voluntarily agreed to the appellate waiver, unless (3) enforcing the waiver would work a miscarriage of justice. Goodson, 544 F.3d at 536; Gwinnett, 483 F.3d at 203.

B.
In determining the scope of a plea agreement's appellate-waiver provision, we are guided by the "well-established principle that `plea agreements, although arising in the criminal context, are analyzed under contract law standards.'" Goodson, 544 F.3d at 535 n. 3 (quoting United States v. Williams, 510 F.3d 416, 422 (3d Cir.2007)). We have explained that, in light of those standards, "the language of [an appellate] waiver, like the language of a contract, matters greatly" to our analysis, Goodson, 544 F.3d at 535, and that such waivers must be "strictly construed." United States v. Khattak, 273 F.3d 557, 562 (3d Cir.2001); cf. Williams, 510 F.3d at 422 ("In view of the government's tremendous bargaining power courts will strictly construe the text [of a plea agreement] against the government when it has drafted the agreement."). But we are also mindful that "[u]nder contract principles, a plea agreement necessarily `works both ways. Not only must the government comply with its terms and conditions, but so must the defendant.'" Williams, 510 F.3d at 422 (quoting United States v. Carrara, 49 F.3d 105, 107 (3d Cir.1995)). Thus, we will not permit a defendant to "`get the benefits of his plea bargain, while evading the costs [because] contract law would not support such a result.'" Id. (quoting United States v. Bernard, 373 F.3d 339, 345 (3d Cir.2004)).
Here, the language of Corso's appellate waiver is broad in scope and clear: Corso agreed to waive the right to take a direct appeal from his conviction or sentence under 28 U.S.C. § 1291 or 18 U.S.C. § 3742 unless (1) the government appealed from the sentence, (2) the sentence exceeded the applicable statutory limits set forth in the United States Code, or (3) the sentence unreasonably exceeded the Guidelines range determined by the District Court under the Sentencing Guidelines. Corso does not claim that either of the first two exceptions applies, conceding, as he must, that the government has not appealed his sentence and that the twenty-one months of imprisonment he received does not exceed the statutory maximum of five years. Nor does he dispute that his sentence is withinindeed, at the bottom ofthe Guidelines range of twenty-one to twenty-seven months determined by the District Court.
Instead, Corso asserts that the appellate waiver's third exception contains an implicit "presumption" that the District Court would "correctly" apply the Guidelines in calculating his Guidelines range, and argues that we may consider his appeal because his twenty-one-month sentence unreasonably exceeds "the correct sentencing range of 4-10 months," i.e., the Guidelines range that results if the number-of-victims *928 and abuse-of-trust enhancements are excluded from the District Court's calculations. Corso accurately notes that our "reasonableness review relies on a district court's reasoning from the starting point of the correctly calculated Guidelines." United States v. Langford, 516 F.3d 205, 213 (3d Cir.2008). But Corso's argument assumes the result he seeks, and we will not review the District Court's application of the sentencing enhancements, or otherwise review his sentence for reasonableness, if he validly waived his right to that review. Cf. Khattak, 273 F.3d at 562 ("`A waiver of the right to appeal includes a waiver of the right to appeal difficult or debatable legal issues indeed, it includes a waiver of the right to appeal blatant error.'" (quoting United States v. Howle, 166 F.3d 1166, 1169 (11th Cir.1999))).
Corso looks for support to the First Circuit's decision in United States v. McCoy, which he cites for the proposition that "a waiver forgoing `any appeal ... if the sentence imposed herein is within the guidelines' does not waive the right to appeal an alleged misapplication of the guidelines." 508 F.3d 74, 78 (1st Cir.2007) (alteration in original) (quoting United States v. Bowden, 975 F.2d 1080, 1081 n. 1 (4th Cir.1992)). But McCoy is inapposite. The narrow appellate-waiver provision at issue in McCoy only barred certain enumerated categories of appeal, including challenges to "any sentence that falls within the guideline range." Id. at 77-78. Because the defendant's challenge to the district court's application of the Guidelines did not fall within that (or any other) enumerated category, it was necessarily permitted. Id. at 78. Corso's appellate waiver, in contrast, is broad, and an appeal that does not fall within one of its three narrow exceptions is necessarily waived.
Moreover, Corso ignores the plain text of his waiver's third exception which, unlike the language at issue in McCoy, permits appeal only if "the sentence unreasonably exceeds the guideline range determined by the Court under the Sentencing Guidelines." (Emphasis added). That language explicitly lodges broad discretion in the District Court to determine the applicable Guidelines range; it certainly does not permit an appeal challenging the District Court's application of the Guidelines. We conclude, therefore, that Corso's appeal falls within the scope of his appellate waiver.

C.

1.
We must next consider Corso's argument that his waiver was not knowing and voluntary because the District Court violated Federal Rule of Criminal Procedure 11(b)(1)(N), which requires a court, before accepting a guilty plea, to "address the defendant personally in open court. During this address, the court must inform the defendant of, and determine that the defendant understands ... the terms of any plea-agreement provision waiving the right to appeal or to collaterally attack the sentence." Corso contends that the District Court failed during its colloquy with him at the change-of-plea hearing both to adequately inform him of the terms of his appellate waiver and to ensure that he understood those terms.
Because Corso did not object before the District Court to its purported Rule 11 error, he "has the burden to satisfy the plain-error rule," Vonn, 535 U.S. at 59, 122 S.Ct. 1043, and must show (1) that there was an error, i.e., a deviation from a legal rule, (2) that the error was "plain," i.e., clear or obvious, and (3) that the error affected his substantial rights. See Johnson *929 v. United States, 520 U.S. 461, 467, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997); United States v. Olano, 507 U.S. 725, 732-34, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993); see also Goodson, 544 F.3d at 539. But "relief on plain-error review is in the discretion of the reviewing court," and even if all three conditions are met we will exercise our discretion to correct the unpreserved error only if Corso persuades us that (4) "a miscarriage of justice would otherwise result," that is, if "the error seriously affect[ed] the fairness, integrity or public reputation of judicial proceedings." Olano, 507 U.S. at 736, 113 S.Ct. 1770; see Vonn, 535 U.S. at 63, 122 S.Ct. 1043; Johnson, 520 U.S. at 467, 117 S.Ct. 1544. We may consult the entire record, and not simply the record of the plea colloquy, when considering the effect of the Rule 11 error. Vonn, 535 U.S. at 59, 122 S.Ct. 1043; see also Goodson, 544 F.3d at 540.

2.
Corso has unquestionably met his burden under the first two prongs of the plain-error analysis. Our review of the record indicates that the District Court did not personally discuss the appellate waiver with Corso, or even mention the waiver at any point, depending instead on the prosecutor to "outline" the plea agreement during the change-of-plea hearing. But nothing in the plain language of Rule 11(b)(1) permits a district court to delegate its responsibilities to "inform" and "determine" to the government; the Rule provides that "the court must" do both of those things. And even presuming that the District Court was permitted to rely on the government in this manner, the prosecutor's cursory aside that Corso's plea agreement "contains the standard language regarding waiver of appeal in that it sets forth the only exceptions to it" was plainly insufficient, adding little to the District Court's complete silence on the subject. These failures were clearly error. Cf. Goodson, 544 F.3d at 540 (finding that the district court erred both when it "relied upon the prosecutor's recitation of the terms of the appellate waiver to fulfill its obligation to inform the defendant of the specifics of the waiver provision" and when it failed to verify that the defendant understood the waiver).

3.
We then turn to the third prong of the plain-error analysis, which requires Corso to show that his substantial rights were affected by these errors. The Supreme Court has held that, in order to demonstrate that substantial rights were affected, "a defendant who seeks reversal of his conviction after a guilty plea, on the ground that the district court committed plain error under Rule 11, must show a reasonable probability that, but for the error, he would not have entered the plea." United States v. Dominguez Benitez, 542 U.S. 74, 83, 124 S.Ct. 2333, 159 L.Ed.2d 157 (2004); see United States v. Hall, 515 F.3d 186, 194 (3d Cir.2008). But where, as here, the defendant does not seek the reversal of his conviction (i.e., does not seek to withdraw his guilty plea) but only challenges the validity of his appellate waiver so that he may appeal from his sentence, he is obliged to show a reasonable probability that the Rule 11 error "precluded him from understanding that he had a right to appeal and that he had substantially agreed to give up that right." Goodson, 544 F.3d at 541; see also United States v. Sura, 511 F.3d 654, 662 (7th Cir.2007) ("If the safeguard required by Rule 11 is missing, the record must reveal an adequate substitute for it, and the defendant must show why the omission made a difference to him."); United States v. Murdock, 398 F.3d 491, 497 (6th Cir.2005) (holding that "a defendant can prove that *930 his substantial rights are affected when he shows that the district court failed to comply with the key safeguard in place to protect those rights and that there was no functional substitute for that safeguard"); but cf. United States v. Borrero-Acevedo, 533 F.3d 11, 18 (1st Cir.2008) (holding that a defendant "must show that the waiver of appellate rights was deficient and that he would otherwise not have pled guilty" in order to meet the burden to show that substantial rights are affected). "The reasonable-probability standard is not the same as, and should not be confused with, a requirement that a defendant prove by a preponderance of the evidence that but for error things would have been different." Dominguez Benitez, 542 U.S. at 83 n. 9, 124 S.Ct. 2333.
In Goodson, we addressed some of the considerations that inform our inquiry into whether an inadequate Rule 11 colloquy affected a defendant's substantial rights. In that case, the evidence in the record demonstrated that the defendant was "college educated," had "successfully perpetrated wire fraud and the uttering of counterfeit checks," and "was able to read the plea letter and to comprehend the meaning of its provisions." 544 F.3d at 540-41. Importantly, the record also demonstrated that "the prosecutor generally discussed the terms of the appellate waiver" during the change-of-plea hearing and that the defendant "advised the Court that he understood that his right to appeal was substantially limited." Id. at 541. We also noted that the defendant "had executed the acknowledgment on the final page of his plea agreement, indicating that he had read the agreement, which included the appeal waiver, and discussed it with his counsel." Id. Under those circumstances, we concluded that the defendant had failed to meet his burden under the third prong of the plain-error analysis. Id.
In this case, the record demonstrates that Corso, like the defendant in Goodson, signed his plea agreement, confirming that he had read the agreement and discussed it with his attorney. But "[t]he point of Rule 1 1(b)(1)(N) is that a signed piece of paper is not enough," Sura, 511 F.3d at 662, and the District Court made no effort to determine that Corso, whose education is limited to a GED diploma, understood the effect of his waiver on his right to appeal, or even whether he had discussed the waiver with his attorney.[2] And the prosecutor's fleeting reference to "the standard language regarding waiver of appeal," without further exposition, can hardly be deemed a "discussion" of the terms of Corso's appellate waiver, much *931 less an adequate substitute for the missing safeguards of Rule 11(b)(1)(N). Cf. Goodson, 544 F.3d at 541; United States v. Robinson, 455 F.3d 602, 610 (6th Cir.2006) (concluding that "substitutes for Rule 11 compliance" were present where the prosecutor thoroughly explained the appellate-waiver provision at the court's request and the court independently ascertained that the defendant understood the provision and had discussed "all of the provisions" in the plea agreement with his attorney). "In determining whether a waiver of appeal is `knowing and voluntary,' the role of the sentencing judge is critical." Khattak, 273 F.3d at 563; cf. United States v. Schweitzer, 454 F.3d 197, 205 (3d Cir.2006) ("There is simply no substitute for on-the-record discussion and deliberation."). Informed by the entire record, we are satisfied that Corso has carried his burden to show that the District Court's near-total deviation from the mandates of Rule 1 1(b)(1)(N) affected his substantial rights.

4.
But a clear error affecting substantial rights cannot, "without more," satisfy the fourth prong of the plain-error analysis, Olano, 507 U.S. at 737, 113 S.Ct. 1770, and the Supreme Court has instructed that we are authorized "to correct only particularly egregious errors" on plain-error review. United States v. Young, 470 U.S. 1, 15, 105 S.Ct. 1038, 84 L.Ed.2d 1 (1985). We do not believe that Corso has established that the District Court's deficient colloquy seriously affected the fairness, integrity, or public reputation of the judicial proceedings.
Corso also argues that we should exercise our remedial discretion to set aside his appellate waiver because the District Court's application of the number-of-victims and abuse-of-trust enhancements in calculating his Guidelines range constitutes a "miscarriage of justice." But Corso's focus on alleged procedural errors in the determination of his sentence is misplaced, and demonstrates "`the logical failing of focusing on the result of the proceeding, rather than on the right relinquished, in analyzing whether an appeal waiver is valid.'" United States v. Smith, 500 F.3d 1206, 1213 (10th Cir.2007) (quoting United States v. Hahn, 359 F.3d 1315, 1326 n. 12 (10th Cir.2004)). Procedural errors of this nature cannot justify setting aside an appellate waiver because "allow[ing] alleged errors in computing a defendant's sentence to render a waiver unlawful would nullify the waiver based on the very sort of claim it was intended to waive." Id. Although the right to appeal is one "of critical importance to a criminal defendant," Murdock, 398 F.3d at 498, we are unconvinced, on the record here, that enforcing the appellate waiver in Corso's plea agreement would result in a miscarriage of justice. See Olano, 507 U.S. at 736, 113 S.Ct. 1770; Johnson, 520 U.S. at 470, 117 S.Ct. 1544; cf. United States v. Arellano-Gallegos, 387 F.3d 794, 797 (9th Cir.2004) (holding that enforcement of appellate waiver "would seriously affect the fairness, integrity and public reputation of our plea proceedings" where there was a "`wholesale failure' to comply with Rule 11 or otherwise ensure that [the defendant] understood the consequences of waiving his right to appeal the sentence which had yet to be imposed").[3]*932 Accordingly, we will enforce Corso's appellate waiver and do not reach the merits of this appeal.

IV.
For the foregoing reasons, we will affirm the judgment of the District Court.
NOTES
[1]  Application Note 4(C)(ii)(I) provides in relevant part: "Special Rule.A case [involving the theft or attempted theft of United States mail from] a United States Postal Service relay box, collection box, delivery vehicle, satchel, or cart, shall be considered to have involved at least 50 victims." U.S.S.G. § 2B1.1 cmt. n. 4(C)(ii)(I).
[2]  As Corso indicates in his brief, the District Court later compounded these clear errors when it unequivocally told Corso at the end of the sentencing hearing that he had a "right to appeal" his sentence. We acknowledge that the District Court may have felt obligated to make those statements due to Federal Rule of Criminal Procedure 32(j)(1)(B), which requires a court, "regardless of the defendant's plea," to advise the defendant after sentencing of "any" right to appeal the sentence. But we believe that the District Court should have qualified its post-sentencing remarks, ideally by explaining to Corso that his appellate waiver, if valid, curtailed his ability to appeal issues within its scope. At the very least, the District Court should have acknowledged the existence of the appellate waiver and its narrow exceptions. Cf. United States v. Tang, 214 F.3d 365, 370 (2d Cir.2000) (explaining that sentencing judges "should not give unqualified advice concerning a right to appeal" in cases involving an appellate waiver). Nonetheless, such post-sentencing remarks do not per se "render ineffective an otherwise enforceable waiver of appellate rights.... [A] waiver does not lose its effectiveness because the district judge gives the defendant post-sentence advice inconsistent with the waiver [because] no justifiable reliance has been placed by the defendant on such advice." United States v. Liriano-Blanco, 510 F.3d 168, 173 (2d Cir.2007).
[3]  We note that it is an open question whether, or the extent to which, our analysis under the fourth prong of the plain-error rule overlaps our other inquiry, guided by the non-exclusive list of factors identified in United States v. Khattak, 273 F.3d 557, 563 (3d Cir.2001), into "whether enforcing [an appellate] waiver would work a miscarriage of justice." United States v. Jackson, 523 F.3d 234, 244 (3d Cir. 2008) (citing Khattak, 273 F.3d at 562 and United States v. Gwinnett, 483 F.3d 200, 203 (3d Cir.2007)). We need not resolve that question here, however, because we conclude that enforcing Corso's appellate waiver would not result in a miscarriage of justice under either the plain-error rule or Khattak and its progeny.
