I. Background

E.F. pleaded guilty to a number of federal offenses pursuant to a plea agreement. Under the terms of the plea agreement, the government agreed that it would recommend a sentence below the one recommended by the United States Sentencing Guidelines.

As a result of that agreement, the district court significantly reduced E.F.'s advisory guidelines range to approximately half the term of imprisonment recommended by the Guidelines. E.F. was ultimately sentenced to the mandatory minimum sentence. The district court noted it would have preferred to sentence E.F. to a lesser sentence, but it was unable to do so in light of the government's refusal to file a motion for a further reduction pursuant to 18 U.S.C. § 3553(e), which authorizes the district court to impose a sentence below the statutory mandatory minimum for substantial assistance.

The district court first considered whether United States v. Doe , 865 F.3d 1295 (10th Cir. 2017), applies. In Doe , we held that in certain circumstances, the government's decision not to file a substantial-assistance motion pursuant to USSG § 5K1.1 is subject to good-faith review. The court concluded that while Doe applies, E.F. failed to satisfy the Doe requirements that would trigger good-faith review by the district court. Thus, the plea agreement was not subject to good-faith review.

As we explain, we agree with the district court's analysis under Doe and affirm its conclusion that the government's decision not to file a § 3553(e) motion is not subject to good-faith review.

II. Analysis

E.F. raises three arguments for reversal. First, E.F. contends that the government breached the covenant of good faith and fair dealing implied in the plea agreement when it refused to file a § 3553(e) motion. Similarly, E.F. contends the government's refusal was not rationally related to a legitimate government end and that enforcing the plea agreement would result in a miscarriage of justice. Finally, E.F. argues that the sentence was substantively unreasonable.

A. Application of Doe

Courts "review de novo whether the [g]overnment has breached a plea agreement." United States v. Rodriguez-Rivera , 518 F.3d 1208, 1212 (10th Cir. 2008). While the government initially argued the standard of review is plain error because E.F. did not sufficiently allege a breach of the plea agreement in the district court, the government did not reassert this argument following the district court's decision to apply Doe . Furthermore, as discussed below, E.F. sufficiently raised the good-faith issue, and we therefore review de novo the district court's analysis under Doe .

Under the terms of the plea agreement in Doe , the government was obligated *686to exercise its discretion in determining whether to file a substantial-assistance motion as permitted by USSG § 5K1.1 or § 3553(e). The government exercised its discretion and declined to file either motion. But the defendant argued the government failed to exercise its discretion in good faith, thus raising the question of whether the government's discretionary decisions can be reviewed for breach of contract. We agreed a duty of good faith applied to plea agreements. To be entitled to good-faith review in district court, (1) the defendant must first allege that the government acted in bad faith; (2) the government can then rebut the allegation by providing justifications for its refusal to file the motion; and (3) the defendant must then produce evidence "giving reason to question the justification" advanced by the government. Doe , 865 F.3d at 1300. If the defendant succeeds at step three, the court will proceed to a merits determination as to whether the government breached the plea agreement.

But this case is different from Doe because it only involves the government's discretionary decision to refuse to file a substantial-assistance motion under § 3553(e). While the government here refused to file a substantial assistance motion pursuant to the statute, it did move for a sentence reduction pursuant to § 5K1.1 of the Guidelines. E.F. argues the government should have moved for both a § 5K1.1 reduction and a § 3553(e) reduction.

At a minimum, Doe stands for the proposition that if a prosecutor files no motion at all for substantial assistance, then the district court may conduct good-faith review if certain conditions are met. E.F. argues Doe stands for more- Doe means prosecutorial discretion to file neither, either, or both motions is always subject to good-faith review if the additional conditions are met.

Doe states "a prosecutor's discretionary refusal to file a substantial-assistance motion"-so the question is whether review is only triggered when a prosecutor refuses to file either type of motion, as was the case in Doe , or if review can also be triggered when a prosecutor files one type but refuses to file the other type of motion. Doe , 865 F.3d at 1300. The district court extended Doe to include the latter. The district court said the good-faith review outlined in Doe applies in cases where the prosecutor declines to file one type of substantial-assistance motion-even if the prosecutor files another type of substantial-assistance motion. This makes sense given that a § 3553(e) motion crucially allows a district court to go below the statutory mandatory minimum. According to the district court, this difference compels good-faith review when the government could file both a § 5K1.1 and a § 3553(e) motion but only chooses to file a § 5K1.1 motion.1 For purposes of this appeal, we assume Doe applies.

In applying Doe 's three-step analytical framework, the district court assumed E.F. satisfied the first step. But the district court found persuasive the government's explanation for refusing to file a § 3553(e) motion-that prosecutors discovered evidence of ongoing criminal activity. Thus, E.F. failed to rebut the government's explanation at the third step. Because E.F. did not rebut the government's explanation, the district court found that it need not proceed to a full merits review of the government's good faith.

*687E.F. argues that the district court improperly applied Doe because the government failed to provide a facially plausible explanation for its failure to file a § 3553(e) motion. Even if it did, E.F. adequately rebutted the presumption and the court should hold an evidentiary hearing on the allegations.

Before addressing this argument, we turn first to the government's argument that E.F. failed to preserve the bad-faith breach theory in the district court. Doe , 865 F.3d at 1300. In the initial district court proceedings, E.F. objected to the government's failure to file a motion under § 3553(e) in the response to the government's § 5K1.1 motion. While E.F. did not use the words "breach," or accuse the government of operating in "bad faith," it was clearly argued that the government had an obligation to determine in good faith how to reward substantial assistance. The parties discussed the nature of E.F.'s substantial assistance and acknowledged that the government only moved for a § 5K1.1 motion. After the discussion, the district court expressed its displeasure with the government's failure to file a § 3553(e) motion for downward departure.

All that is required to preserve an issue for appeal is that the party "inform[s] the court [of] the party's objection to the court's action and the grounds for that objection." Fed. R. Crim. P. 51(b). E.F. responded to the government's § 5K1.1 motion, the parties discussed the motions at sentencing, and the district court acknowledged that the government's failure to file a § 3553(e) motion was problematic. This all indicates that E.F. properly raised the issue in the district court. To find otherwise would promote form over substance-rather, the sole question is "whether the district court was adequately alerted to the issue." United States v. Harrison , 743 F.3d 760, 763 (10th Cir. 2014). Because the district court was aware E.F. thought the government failed to act in good faith, we find that E.F. sufficiently alleged bad faith, satisfying the first part of the Doe analysis. See Chalfonte Condo. Apartment Ass'n, Inc. v. QBE Ins. Corp. , 695 F.3d 1215, 1225 (11th Cir. 2012) (noting that the absence of good faith is bad faith).

The second issue is whether the government presented a plausible explanation for not filing a § 3553(e) motion. The court agreed that the government had reason to believe E.F. was not completely candid in discussions leading up to the sentencing hearing. Specifically, the court concluded E.F. did not reveal ongoing criminal activity related to the federal charges. While the exact details of what the government knew or did not know when it entered into the plea agreement are not entirely clear, it is clear that-even after the plea agreement was signed-the government continued to uncover more evidence of E.F.'s wrongdoing. The government, therefore, provided a plausible justification for its decision not to move for a downward departure under § 3553(e).

The government expected full cooperation, which is why it offered to move for departures under both § 3553(e) and § 5K1.1. The parties do not dispute the fact that E.F. substantially cooperated, and the government admits the cooperation was instrumental in their investigation. But full cooperation surely requires disclosing valuable information, particularly about ongoing criminal activity. The government had discretion to decide whether to file a § 3553(e) motion. E.F. did cooperate partially with officials, but the evolving standards of candor brought into question E.F's credibility as a potential witness. Accordingly, the government chose to file a § 5K1.1 motion rather than a § 3553(e) motion.

*688E.F. claims the doctrine of judicial admissions prevents the government from justifying the prosecutor's decision not to file a § 3553(e) motion because the government failed to raise the justifications until after the district court initially sentenced E.F. "Judicial admissions are formal admissions ... which have the effect of withdrawing a fact from issue and dispensing wholly with the need for proof of the fact." Guidry v. Sheet Metal Workers Int'l Ass'n, Local No. 9 , 10 F.3d 700, 716 (10th Cir. 1993), abrogated by Estate of Cummings v. Cmty. Health Sys., Inc. , 881 F.3d 793 (10th Cir. 2018). They are "formal, deliberate declarations which a party or his attorney makes in a judicial proceeding for the purpose of dispensing with proof of formal matters or of facts about which there is no real dispute." U.S. Energy Corp. v. Nukem, Inc. , 400 F.3d 822, 833 n.4 (10th Cir. 2005). Judicial admissions are not just any statements made before the court.

The government's proffered justifications at sentencing were not "deliberate declarations" and were not about facts "about which there is no real dispute." Nukem , 400 F.3d at 833 n.4. The government offered several reasons why it did not file a § 3553(e) motion, but it did so without the benefit of Doe and only in response to E.F.'s suggestion of lack of good faith. Judicial admissions more appropriately refer to "admissions in the pleadings" that "are binding on the parties." Mo. Hous. Dev. Comm'n v. Brice , 919 F.2d 1306, 1315 (8th Cir. 1990). Discussions at sentencing, particularly on unresolved legal questions, differ from judicial admissions in the pleadings. See Martinez v. Bally's La., Inc. , 244 F.3d 474, 476 (5th Cir. 2001) ("A statement made by counsel during the course of trial may be considered a judicial admission if it was made intentionally as a waiver, releasing the opponent from proof of fact."). After Doe was decided, the government raised the justifications to satisfy its burden to show why it did not file a § 3553(e) motion.2

Finally, the third step of the Doe analysis requires E.F. to provide evidence calling into question the government's justifications. E.F. argues the government knew of the ongoing criminal activity before the plea agreement was signed. According to E.F., because the government represented that a § 3553(e) motion was possible-even with knowledge of the ongoing criminal activity-the government's explanations fall short of the requisite standard.

We evaluate the plea agreement "in light of the defendant's reasonable understanding of the promise at the time of the guilty plea." United States v. Rodriguez-Delma , 456 F.3d 1246, 1250 (10th Cir. 2006). At the time the plea agreement was signed, the government was still investigating ongoing criminal activity. In the plea agreement, E.F. agreed to provide full, complete, and truthful cooperation. But E.F. admitted to failing to disclose the ongoing criminal activity, which was fully discovered after the plea agreement was signed. Even though we now know the ongoing criminal activity never materialized beyond the planning stage, the government had reason not to fully reward E.F. by filing two motions. E.F. does not provide any evidence beyond the initial discovery of the criminal activity that would call the government's justifications into question.

*689Ultimately, under the Doe analysis, E.F.'s allegations do not trigger good-faith review of the plea agreement. While E.F. successfully alleged that the government breached the plea agreement, the government provided adequate justifications that E.F. failed to rebut.

Therefore, the government's discretionary refusal to file a § 3553(e) motion, in addition to its § 5K1.1 motion, is not subject to good-faith review.

B. Motion to Enforce Appellate Waiver

The government asks us to enforce E.F.'s waiver of the right to appellate review if we agree the plea agreement was not breached under Doe .

We ordinarily enforce appeal waivers that are entered knowingly and voluntarily. Our review considers "(1) whether the disputed appeal falls within the scope of the waiver of appellate rights; (2) whether the defendant knowingly and voluntarily waived his appellate rights; and (3) whether enforcing the waiver would result in a miscarriage of justice." United States v. Hahn , 359 F.3d 1315, 1325 (10th Cir. 2004).

All three Hahn factors are met here. The plea agreement clearly stated that E.F. "knowingly and voluntarily ... waives the right to directly appeal the conviction and sentence," and E.F. confirmed an understanding of the agreement at the plea hearing.

As to the third factor-miscarriage of justice-E.F. argues the government's concession about substantial assistance and its failure to follow through with its promise for leniency at sentencing establishes a miscarriage of justice. E.F. relies on United States v. Lukse , 286 F.3d 906 (6th Cir. 2002), where the court held the government was required to file a substantial assistance motion once it determined substantial assistance was rendered. In that case, the government stated in the plea agreement that it would file a substantial assistance motion if, in its discretion, it determined the defendant rendered substantial assistance. Id. at 912. E.F. argues securing a guilty plea that includes a waiver of appeal in exchange for an illusory promise affects the fairness and integrity of the plea agreement process. But Lukse is distinguishable. In this case, the government, in fact, filed a substantial-assistance motion under § 5K1.1-just not the kind of additional substantial-assistance motion E.F. wanted under § 3553(e). Furthermore, the issue in Lukse was not whether the appellate waiver was enforceable, but whether the court could review the government's failure to file a downward departure. Lukse does not speak to the waiver issue. Since we have concluded the government's refusal to file an additional motion for a reduced sentence is not subject to good-faith review, E.F. cannot meet the third element of Hahn.

In sum, a within-guidelines sentence is not a miscarriage of justice. Rita v. United States , 551 U.S. 338, 347, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007) (holding that a within-guidelines sentence is presumptively reasonable). E.F. was sentenced to the mandatory minimum term of imprisonment as sanctioned by Congress, which falls directly within the applicable guidelines range. E.F. gives no other reason why the plea agreement was "otherwise unlawful" or seriously impacted "the fairness, integrity or public reputation of judicial proceedings." Hahn , 359 F.3d at 1329. Therefore, the appellate waiver is enforceable, and we grant the government's motion.

III. Conclusion

For the reasons stated above, we affirm the district court's finding that the plea *690agreement is not subject to good-faith review under Doe . Because the application of Doe does not trigger good-faith review, we conclude the government was within its discretion in not filing a § 3553(e) motion. Thus, E.F.'s only remaining claim is that the sentence imposed is substantively unreasonable. The sentence was within the guideline range, so this appeal falls within the scope of the appellate waiver, which was made knowingly and voluntarily. We therefore grant the government's motion and enforce the appellate waiver.