We do not know whether Ricky Olson entered a voluntary and intelligent guilty plea on September 9, 2016, because the district court never asked the right questions. Several weeks earlier, the court had granted Olson’s motion to withdraw his guilty plea and to proceed to trial. But matters did not rest there. Instead, on September 9 the district court brought the motion to withdraw the guilty plea back to life (that is, the one it had already disposed of), and this time summarily denied it. The court ultimately sentenced Olson to 180 months of incarceration and 20 years of supervised release. On appeal, Olson complains that the .irregular proceedings surrounding his plea failed to comply with the rules of criminal procedure. We agree with him. Because the September 9 proceedings resulted in a new. change of plea, which the district court accepted without conducting the colloquy required by Federal Rule of Criminal Procedure 11, we reverse and remand.

I

Olson was convicted on charges of distributing sexually explicit photographs of his minor daughter in violation of 18 U.S.C. § 2252 (a)(2). Our concern, however, is not with the facts that lie behind his conviction, nor is it with any defense he plausibly might raise. It is with the procedure the court followed in obtaining the guilty plea on which it relied. Olson argues that the court committed plain error by reactivating Olson’s earlier guilty plea and then accepting that plea without conducting a proper colloquy under Rule 11.

Olson first pleaded guilty to violating Section 2252(a)(2) on April 6, 2016. As part of an accompanying plea agreement, he stipulated to conduct charged in three other counts of his indictment and waived the right “to appeal his conviction and any sentence of imprisonment of 180 months or less.” In' exchange, the government promised to dismiss all charges not covered by his guilty plea. Before accepting the plea on April 6, the district court conducted a Rule 11 colloquy. Part of Olson’s current appeal is an attack on that exchange as inadequate and plainly erroneous. He directs our attention to a confused discussion about whether the images were “sexually explicit” as required by section 2252(a)(2). Although Olson eventually conceded that the .photographs showed his daughter *876 naked, he repeatedly denied that they were sexually explicit, showed his daughter’s vagina or depicted her masturbating, and he stated that he “d[id]n’t understand” the court’s questions. Despite this confusion, the court accepted the plea.

At an ex parte hearing on August 26, 2016, Olson moved to withdraw his guilty plea, and his attorney, Peter Moyers, moved to withdraw from representation. The district court orally granted both motions and memorialized its ruling in writing. Olson complained at the hearing that he had not understood the plea agreement, had pleaded under pressure from his attorney, and had not thought that the images were sexually explicit. Moreover, according to Olson, the theft of his glasses while he was in prison had prevented him from reading his plea agreement before signing it. As a result, he asserted, the agreement had been “kind of paraphrased” for him. Olson further maintained that he had not understood his potential sentence and had not known he would qualify as a sex offender. He displayed confusion over what crimes were covered by his April 6 plea. > At one point he even suggested that he had pleaded guilty to four charges that the plea agreement in fact required the government not to pursue. Olson claimed that he had pleaded guilty despite his belief that the photographs were not sexually explicit only after his attorney had flatly instructed him to “[p]lead guilty. The DA is just mistaken, we’ll hash all that out later.” Olson complained that Moyers refused to file objections to the presentence report, warning Olson that, if Moyers did object, the judge would impose a 30-year sentence on Olson. Moyers equated this term to “a life sentence” or dying in prison. (We stress that none of these allegations about Moyers’s performance has been substantiated; we nonetheless present Olson’s subjective view because it informed the district court’s decision to grant his motion and informs our review of the intelligence and voluntariness of his plea.)

At Olson’s request, an additional plea-related hearing took place on September 9. Joe Bugni, rather than Moyers, now represented him. During a brief exchange, Olson stated that he was “definitely guilty of one charge” and expressed a belief that his “best course [was] just to throw [him]self at the mercy of the court.” Without further ado, the district court then announced it would move forward with sentencing. At Bugni’s prompting, the court also purported to deny the already-granted August 26 motion to withdraw Olson’s guilty plea and Moyers’s motion to withdraw from representation (though Moyers never reappeared, and Bugni continued to represent Olson). On that occasion, the court did not hold a Rule 11 colloquy or anything resembling one.

The district court .sentenced Olson on September 26 and entered final judgment that day. He now appeals both his conviction and sentence. Olson argues that the district court plainly erred by dispensing with a Rule 11 colloquy on September 9, when he indicated his willingness to plead guilty. In the alternative, he asks that we vacate his sentence because of the court’s failure to calculate the guidelines range and consider the factors in 18 U.S.C. § 3553 (a) before imposing a term of supervised release.

II

Rule 11 of the Federal Rules of Criminal Procedure requires a trial court to “address the defendant personally in open court” before accepting his guilty plea. Fed. R. Cbim. P. 11(b). During this colloquy, the court must convey specific information about his rights and the consequences of his plea; and it must satisfy itself that he understands those rights. Fed. R. Crim. P. 11(b)(1). The court also must ensure that the plea is voluntary, *877 Fed. R. Crim. P. 11(b)(2), and that it is supported by a factual basis, Fed. R. Crim. P. 11(b)(3). While not itself of constitutional dimension, Rule 11 helps to ensure compliance with the constitutional rule that a guilty plea must be knowing and voluntary. McCarthy v. United States, 394 U.S. 459 , 465, 467, 89 S.Ct. 1166 , 22 L.Ed.2d 418 (1969), superseded on other grounds by rule, Fed. R. Crim. P. 11(h), as recognized in United States v. Cross, 57 F.3d 588 , 591 (7th Cir. 1995); see also Boykin v. Alabama, 395 U.S. 238 , 242-43, 89 S.Ct. 1709 , 23 L.Ed.2d 274 (1969). The rule also aids appellate review by creating a contemporary record. McCarthy, 394 U.S. at 465, 467 , 89 S.Ct. 1166 . In order to plead intelligently in the constitutional sense, a defendant “must understand not only the nature of the charge ... but also that his or her conduct actually falls within the charge.” United States v. Frye, 738 F.2d 196 , 199 (7th Cir. 1984).

Because Olson raised no objection to the district court’s method of proceeding, we review the court’s deviation from the strictures of Rule 11(b) for plain error. United States v. Vonn, 535 U.S. 55 , 58, 122 S.Ct. 1043 , 152 L.Ed.2d 90 (2002); see Fed. R. Crim. P. 11(h). Therefore, Olson bears the burden of showing: (1) an error, (2) that is plain or obvious, (3) that affects his “substantial rights,” and (4) that “seriously affect[s] the fairness, integrity, or public reputation of judicial proceedings.” Puckett v. United States, 556 U.S. 129 , 135, 129 S.Ct. 1423 , 173 L.Ed.2d 266 (2009); United States v. Anderson, 604 F.3d 997 , 1002 (7th Cir. 2010).

A

As a preliminary matter, we reject the government’s view that Olson entered a guilty plea only once, on April 6. According to the government, rather than enter a new guilty plea on September 9, Olson merely moved to withdraw his August 26 motion to withdraw his April 6 guilty plea. Thus, it reasons, on September 9 the district court simply restored the status quo prior to August 26, i.e., the April 6 guilty plea. Because Olson already had pleaded guilty on April 6 and waived no additional rights on September 9, it continues, the district court did not need to engage in a second, redundant Rule 11 colloquy. See, e.g., United States v. Taylor, 984 F.2d 618 , 619 (4th Cir. 1993) (holding no second Rule 11 colloquy mandated when defendant “equivocates about his guilty plea after the initial plea hearing”). The government further argues that the district court conducted a proper Rule 11 colloquy when Olson entered his guilty plea on April 6. Therefore, it concludes, the district court committed no error—plain or otherwise.

The government’s argument fails for a simple reason: Under the circumstances we have outlined, the district court could not “reinstate” the April 6 plea. 1 *878 When Olson filed the September 9 motion, he did not argue that the district court had granted the August 26 motion in error and that the April 6 plea had been fine all along. Indeed, he is still raising objections to the Rule 11 colloquy that accompanied the April plea. That left the “not guilty” plea entered on August 26 as the operative baseline.. The September 9 motion thus had the effect of changing Olson’s plea from “not guilty” to “guilty.” In other words,, the September 9 statement represented a new guilty plea, to which Rule 11 applied independently. E.g., Fed. R. Crim. P, 11(b)(1) (requiring colloquy “[b]efore the court accepts a plea of guilty” (emphasis, added)). In this situation, Rule 11’s requirements are mandatory and plain:, “the court must address the defendant,” “must inform” him of his rights and ensure his understanding, and “must .. determine that the plea is voluntary.” Fed. R. Crim. P, 11(b)(1), (2) (emphasis added). The district court obviously erred by conducting no Rule 11 colloquy on September 9. This satisfies, the first two requirements of plain error review.

The next question is whether the court’s failure to conduct a Rule 11 colloquy on September 9 prejudiced Olson’s substantial rights. When weighing whether a “variance” from Rule 11 affected substantial rights, see Rule 11(h), we consider “whether under the totality of the circumstances, the plea was voluntary and intelligent.” Cross, 57 F.3d at 591 . To prevail, the appellant “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). This test does not demand incontrovertible proof: as we have explained, “[o]ne step ... along the" way to the defendant’s demonstration that the error affected his decision to plead guilty is to look at whether the defendant understood his plea agreement.” United States v. Sura, 511 F.3d 654 , 662 (7th Cir. 2007).

Citing United States v. Vonn, the government contends that the April 6 colloquy serves as evidence that the omission of a Rule 11 colloquy on September 9 was not prejudicial. The government is correct that we must examine the record as a whole when reviewing a particular Rule 11 violation for plain error. As Vonn observes, under some conditions “defendants may be presumed to recall information provided to them prior to the plea proceeding.” 535 U.S. at 75 , 122 S.Ct. 1043 . The question is whether that presumption applies here.

In answering this question, we will assume that Vonn applies to the kind of complete omission of a Rule 11 colloquy that occurred on September 9. Yet, Vonn directs us to consider the entire record, which includes not only the September 9 proceedings, but also the April 6 colloquy (itself arguably insufficient in light of Olson’s professed confusion about the content of the photographs) and the August 26 hearing. Taken as a whole, this record leaves us with serious concern about the intelligence and voluntariness of Olson’s September 9 statements. On August 26, Olson told the court that he had not understood the written plea agreement or the potential sentence, and that he had not believed himself guilty of distributing “sexually explicit” content. While some of his *879 more cogent objections might have indicated an improved understanding of the consequences of pleading guilty, other statements revealed continued confusion and raised voluntariness concerns. For example, while the court permitted Moyers to withdraw as Olson’s attorney, Olson told the court on August 26 that he acted on the advice of prisoners and guards; on September 9 he cited the guidance of fellow inmates. Likewise, while Olson did state that he was “definitely guilty of one charge” on September 9, he never specified which one, Confronted with this vague statement, we recall Olson’s apparent incorrect belief on August 26 that he previously had pleaded guilty to multiple counts and his repeated denial that the images violated section 2262(a)(2), These circumstances give us ho confidence that Olson understood what would follow from his guilty plea of September 9.

And these are not the only signs of a process gone awry. When we review the record, further ambiguities appear. Why did Olson plead guilty on September 9? What did he expect to obtain in return, if anything? Did Olson enter a naked plea, unaccompanied by any agreement, or was the April 6 plea agreement still in force despite the August 26 order? Olson’s own statement that he wished “just to throw [himjself at the mercy of the court” would suggest the former possibility; yet, he, the prosecution, and the district court all seem to have assumed that the plea agreement remained in effect. If he acted on this latter assumption, it was unsupported and inadequate to support his plea.

This court has consistently held that a defendant’s substantial breach of a plea agreement permits the government to rescind the deal. E.g., United States v. Kelly, 387 F.3d 897 , 901 (7th Cir. 2003). We have identified a variety of substantial breaches: for example, absconding before sentencing, United States v. Munoz, 718 F.3d 726 , 729-30 (7th Cir. 2013), refusing to testify against a co-defendant as promised, United States v. Ataya, 864 F.2d 1324 , 1338 (7th Cir. 1988), and failing to comply with an obligation to cooperate with an investigation, Kelly, 337 F.3d at 901-02. Olson’s decision not to plead guilty, had it stuck, would similarly have robbed the government of the benefit of its bargain and forced it to invest substantial resources in trial preparation. In fact, Olson’s August 26 decision to withdraw his guilty plea undermined the agreement’s raison d’être. Therefore, it presumably freed the government to pursue all counts in the indictment. All of this is to say that, as of September 9,. Olson might have had no idea of the consequences of his new guilty plea, and thus might not have entered his plea intelligently. When we as judges cannot determine the legal consequences of Olson’s plea, we decline to conclude that he could.

The final aspect of our plain error analysis looks to the “fairness, integrity, or public reputation of the judicial proceedings.” Anderson, 604 F.3d at 1002 . Safeguarding these values may require that we reverse a conviction “independent of the defendant’s innocence.” United States v. Olano, 507 U.S. 725 , 736-37, 118 S.Ct. 1770 , 123 L,Ed.2d 508 (1993). Our reasoning in United States v. Sura strongly supports reversing the conviction in Olson’s case. In Sura, we held that omitting from a Rule 11 colloquy any discussion of a defendant’s waiver of appellate rights in a plea agreement seriously offended judicial values and was enough to set aside the entire, otherwise knowing, plea agreement. 511 F.3d at 663 . Olson’s potential failure to comprehend the nature of his offense, whether he had committed it, and whether a plea agreement remained effective each justifies setting aside his plea. These are essential aspects of any guilty plea—even *880 more important than the subsidiary condition of the bargain at issue in Sum. Were we to affirm Olson’s conviction and imprisonment under these circumstances, we would undermine confidence in the integrity of the judicial process.

B

Just as we find that Olson did not waive his right to a trial, we hold that he did not waive his right to appeal his conviction. The government first argues that Olson waived this right through an express term in the April 6 plea agreement. Yet an invalid waiver cannot insulate an invalid plea:

Waivers of appeal must stand or fall with the agreements of which they are a part. If the agreement is voluntary, and taken in compliance with Rule 11, then the waiver of appeal must be honored. If the agreement is involuntary or otherwise unenforceable, then the defendant is entitled to appeal.

United States v. Wenger, 58 F.3d 280 , 282 (7th Cir. 1995); see also United States v. Sines, 303 F.3d 793 , 798 (7th Cir. 2002). Thus, in Sura we permitted an appeal despite a waiver, and ultimately set aside the defendant’s underlying guilty plea, because we determined that the plea and related waiver were not intelligently and voluntarily made. 511 F.3d at 657-63 . The same principle holds here. Olson is entitled to challenge his plea on knowledge and voluntariness grounds despite the plea waiver. As we already have discussed, we have no confidence that Olson again entered into the plea agreement on September 9 and, if so, that he did so knowingly and intelligently.

We- also reject the government’s contention that Olson waived his appellate rights by supposedly declining an opportunity to withdraw his guilty plea on September 9. As the government notes, while we treat a failure to file a motion to withdraw a guilty plea as a forfeited claim reviewed for plain error, an “intentional relinquishment or abandonment of a known right” to withdraw a guilty plea “is properly characterized as a waiver of that right” and not subject to appeal. United States v. Davis, 121 F.3d 335 , 338 (7th Cir. 1997). The government argues that Olson’s case is just like Davis, which applied the latter standard. In Davis, the defendant had obtained new counsel after pleading guilty. Id. at 336 . When the new attorney expressed dissatisfaction with his predecessor’s performance, albeit without providing an explanation, the court offered Davis the opportunity to withdraw his guilty plea. Id. After repeated discussion, Davis and his attorney declined that offer, and the case proceeded to sentencing. Id. at 336-37 . On direct appeal, Davis sought to withdraw his guilty plea, arguing for the first time that his original lawyer was conflicted and that his plea was not voluntary and knowing. Id. at 335 . This court treated the issue as waived:

With the advice of counsel and ample opportunity to reflect on the matter, Mr. Davis declined the district court’s invitation to withdraw his guilty plea; he is not entitled to a second bite of the apple by raising on appeal the very matter that he told the district court he did not want to raise.

Id. at 338-39 . The result in Davis was not driven by the defendant’s failure to take the opportunity to withdraw his plea. Rather, the defendant, having obtained new representation, deliberately bypassed the chance to withdraw his plea with full knowledge that the guilty plea was tainted by the misconduct of his former attorney. Nothing prevented him from starting anew.

In stark contrast to Davis, when Olson entered a guilty plea on September 9 the district court’s Rule 11 errors had not yet *881 been cured. In fact, the district court had yet to commit them. The government’s argument to the contrary again rests on the mistaken premise that Olson simply withdrew his August 26 motion and elected to persist with his April 6 plea. We have rejected that characterization of the proceedings. Once the district court ruled on the motion to withdraw the guilty plea on August 26, there was no guilty plea left on the table. On September 9, Olson offered a new guilty plea, but the district court never explored the new plea as required by Rule 11. It never afforded Olson the opportunity to withdraw the September 9 plea, and thus Olson could not have waived his right to do so.

III

Courts’ rulings have meaning. Had the district court opted to take Olson’s August 26 motion under advisement, then when Olson re-appeared on September 9 and stated that he was willing to admit his guilt we might have a different case. But it did not. It granted his motion to withdraw the guilty plea. At that point both the plea and the accompanying agreement were off the table. When Olson had another change of heart, the district court was obliged to conduct a new Rule 11 inquiry. For all we know, the government might have taken the position that it would not renew the earlier agreement and wished to pursue the additional counts of the indictment. Alternatively, the government might have been willing to pick up where it left off in August.

We Reverse Olson’s conviction and Remand his case to the district court for further proceedings consistent with this opinion. Olson must have the opportunity to enter a new plea, either guilty or not guilty, and the government is free to decide whether to pursue a plea agreement. In light of this decision, we have no occasion to consider any procedural short-comings in Olson’s sentencing.