In the midst of his fraud trial, appellant Kevin Reed decided to plead guilty. He was sentenced within the applicable Sentencing Guideline range to sixty-four months in prison. In this appeal, he argues that his guilty plea was involuntary and that the sentencing judge failed to address his principal argument in mitigation, that a prison sentence would impose an extraordinary hardship on his family. We affirm.
I. Factual and Procedural Background
In 2008, Kevin Reed operated Lambert Clark Group and affiliated companies that he claimed were able to make loans of between $50 million and $1 billion to entrepreneurs and start-ups. Reed charged would-be clients advance fees of between $10,000 and $50,000 to apply for these loans. His claims were lies: Reed’s companies had no funds to lend, and while Reed and his co-defendants took in over $200,000 .from six would-be clients, they never closed a loan.
Reed was indicted on six counts of wire fraud in connection with the transmissions of the advance fees. Reed pled not guilty and his case went before a jury. On the morning of the fourth day of trial, though, Reed’s lawyer told the court that Reed wanted to enter a “blind” guilty plea. Per Federal Rule of Criminal Procedure 11, the district judge placed Reed under oath, explained his rights to him, and discussed with him his understanding of the charges and the consequences of pleading to them. Ultimately, the district judge accepted the guilty pleas to all charges.
*471About four months later, and before sentencing, Reed moved to substitute attorneys. His new attorney then moved to withdraw the plea, arguing that Reed’s trial attorney’s ineffective representation at trial had coerced Reed to plead guilty. The district court denied the motion, emphasizing both that Reed had said under oath at his plea colloquy that he was satisfied with his lawyer and that Reed’s claims of ineffectiveness were vague. The case proceeded to sentencing.
Reed’s sentencing memorandum argued for a below-guidelines sentence of probation, emphasizing that his wife (who has a disabling illness) and three children (one of whom also has a disability) depend on him for financial and other forms of support. In a lengthy sentencing hearing, the court heard from Reed’s victims and Reed’s family. The court determined that the Sentencing Guidelines advised a sentence of between fifty-seven and seventy-one months incarceration. The district judge elected to follow that advice and sentenced Reed to sixty-four months in prison.
II. Analysis
We address first Reed’s argument that he should have been allowed to withdraw his guilty plea and second his argument that the judge did not adequately address his mitigation argument based on his family circumstances.
A. Guilty Plea
A defendant may be allowed to withdraw his guilty plea after the court accepts it but before sentencing if he “can show a fair and just reason for requesting the withdrawal.” Fed. R. Crim. P. 11(d)(2)(B). Whether to allow withdrawal is “left to the sound discretion of the district court,” and reversals are rare. United States v. Graf, 827 F.3d 581, 583-84 (7th Cir. 2016) (citations omitted). A motion to withdraw a guilty plea is particularly unlikely to have merit “if it seeks to dispute [the defendant’s] sworn assurances to the court.” Id. at 584.
Appropriate grounds to withdraw a plea include the defendant’s actual or legal innocence, or the involuntary or unknowing nature of the plea. United States v. Mays, 593 F.3d 603, 607 (7th Cir. 2010). Reed argues his plea was involuntary. His theory is that his trial lawyer was so unprepared for trial that he had no alternative but to plead guilty. That claim contradicts Reed’s sworn testimony in his plea colloquy. The district judge asked Reed if he was “fully satisfied with the counsel, representation, and advice” he had been given. Reed replied, “Yes. He’s excellent.” Reed also confirmed that no one had threatened him or attempted “in any way” to force him to plead, and that he was pleading guilty of his “own free will” because he was actually guilty.
Those sworn statements were not “trifles” that Reed could just “elect to disregard.” United States v. Stewart, 198 F.3d 984, 987 (7th Cir. 1999). “A believable claim that the plea had been coerced ... would demonstrate a good reason for deceit,” id., and ineffective assistance of counsel can support such a claim. Graf, 827 F.3d at 584; see also United States v. Weeks, 653 F.3d 1188, 1205-06 (10th Cir. 2011) (defendant’s habeas petition alleged facts entitling him to an evidentiary hearing when it alleged, in part, that counsel’s lack of preparation “pushed him” to enter a guilty plea); United States v. Moore, 599 F.2d 310, 313 (9th Cir. 1979) (“A plea entered because counsel is unprepared for trial is involuntary.”). But the district court did not believe Reed’s claim that his lawyer was ineffective because that claim was so vague.
We agree. Reed provided an affidavit explaining his claim. His affidavit refers to *472“[t]ens of thousands of documents” not used as exhibits and “dozens” of potential witnesses not .interviewed, without identifying one such document or witness, let alone explaining their importance. The affidavit refers to disputing the testimony of an unidentified “key government witness” and to failures to use unspecified “thousands of documents” during unidentified cross-examinations. The affidavit also does not explain why Reed mentioned none of this in his plea colloquy. The affidavit says only that his counsel “prodded” him “to say yes.” Cf. United States v. Jones, 168 F.3d 1217, 1220 (10th Cir. 1999) (“If Defendant was being coerced into pleading guilty, he should have so stated to the district court. He should have asked the court to appoint competent counsel and to continue his trial date.”).
Reed bolsters his argument with a Proposed Defense Trial Plan his trial lawyer filed while seeking to replace Reed’s earlier counsel. That plan laid out a time-line for completing the tasks Reed’s affidavit says were not completed (reviewing unidentified documents, interviewing unspecified witnesses, etc.). The gap between promises and action shows, Reed believes, that his trial lawyer was unprepared. But to show ineffective assistance of counsel, a defendant must show that counsel’s performance was objectively unreasonable. Graf, 827 F.3d at 584 (citations omitted). What Reed wanted from his lawyer or even what his lawyer promised him does not answer that question, nor does the original plan show anything about how plans and expectations may have changed by the time of trial.
The court found that Reed’s vague claims about his lawyer were not “fair and just” grounds to withdraw his plea. The district court did not abuse its discretion in denying leave to withdraw the guilty plea entered in the midst of trial. See Jones, 168 F.3d at 1221 (affirming refusal to permit plea withdrawal based on conclusory claim that counsel was unprepared); United States v. Jones, 381 F.3d 615, 618 (7th Cir. 2004) (motion to withdraw plea can be denied without hearing if the allegations in its support are “mere conclusions”), quoting United States v. Redig, 27 F.3d 277, 280 (7th Cir. 1994).
B. Argument in Mitigation
A sentencing court is required to address the parties’ principal arguments at sentencing, and where a defendant’s principal argument is “not so weak as not to merit discussion,” the court must “explain its reason for rejecting that argument.” United States v. Schroeder, 536 F.3d 746, 755 (7th Cir. 2008), quoting United States v. Miranda, 505 F.3d 785, 792 (7th Cir. 2007). This is a procedural requirement “designed to ensure that the judge has in fact considered the principal issues affecting the sentencing decision.” United States v. Donelli, 747 F.3d 936, 940 (7th Cir. 2014). It also allows the reviewing court to satisfy itself that the judge considered those issues. Id. at 939.
Our cases applying this procedural requirement do not draw a bright line to tell district judges when they have said enough, but “we try to take careful note of context and the practical realities of a sentencing hearing. District judges need not belabor the obvious.” United States v. Castaldi, 743 F.3d 589, 595 (7th Cir. 2014), quoting United States v. Gary, 613 F.3d 706, 709 (7th Cir. 2010). To avoid issues about the adequacy of an explanation, “we encourage sentencing courts to inquire of defense counsel whether they are satisfied that the court has addressed their main arguments in mitigation.” United States v. Garcia-Segura, 717 F.3d 566, 569 (7th Cir. 2013); see also, e.g., Donelli, 747 F.3d at 940 (finding defense waived argument *473about adequacy of sentencing judge’s explanation). That did not happen here.
The Sentencing Guidelines advise that a defendant’s family ties and responsibilities are not ordinarily relevant in deciding whether to depart from the guideline range. See U.S.S.G. § 5H1.6. Every sentencing judge knows that a prison sentence will impose hardships on an offender’s family. Every judge has heard heartrending accounts of those hardships. The most common response is to acknowledge those hardships and to remind both the offender and his family that the hardship was caused by the offender’s decision to commit the crimes for which he is being sentenced.
Nevertheless, truly extraordinary family circumstances can provide a legitimate basis for a lighter or below-guideline sentence, whether under § 5H1.6 or the sentencing court’s broader discretion and responsibility under 18 U.S.C. § 3553(a). See Schroeder, 536 F.3d at 755. Reed asked the district court for a below-guideline sentence on that basis, emphasizing his wife’s and one son’s disabilities, that he has two other children, and that he was the family’s only financial support.
One can argue how extraordinary these circumstances actually were, but the argument deserved to be addressed, especially since it was Reed’s lead argument at sentencing. The district judge was therefore required to address it, although he could do so briefly or even “implicitly” or “imprecisely.” United States v. Diekemper, 604 F.3d 345, 355 (7th Cir. 2010); United States v. Poetz, 582 F.3d 835, 839 (7th Cir. 2009) (judge’s discussion at sentencing, although “perhaps imprecise,” undermined claim that judge “overlooked or ignored” defendant’s “family-hardship argument”); Schroeder, 536 F.3d at 755 (“A short explanation will suffice where the context and record make clear the reasoning....”). The key question is whether the reviewing court can have “confidence in the judge’s considered attention to the factors in this case.” United States v. Cunningham, 429 F.3d 673, 679 (7th Cir. 2005).
Standing alone, the transcript of the sentencing hearing does not give us that confidence. The judge discussed how Reed’s family reflected his character, noting that he had been a “wonderful” father, husband, and brother, which is often true in such white-collar fraud cases. But the judge did not mention the family’s particular medical or financial needs or acknowledge the hardships imprisonment would create for them. Even viewing the hearing as a whole, we are not convinced that the judge addressed this point sufficiently in the hearing. Cf. Castaldi, 743 F.3d at 596 (judge adequately addressed mitigation argument when he mentioned it at hearing’s start, engaged with defense counsel’s final argument emphasizing issue, and said he had considered all mitigation arguments).
The best time to address principal mitigation arguments is in the sentencing hearing itself. See 18 U.S.C. § 3553(c) (“The court, at the time of sentencing, shall state in open court the reasons for its imposition of the particular sentence ....”). That allows the court to obtain defense counsel’s input on whether those arguments were addressed adequately and assures us that important mitigation arguments were not rationalized away after the fact. That said, we have also “encouraged district courts to commit their sentencing decisions to paper,” and we read a district court’s written statement of reasons “as an aid to the interpretation of its oral statement.” United States v. Pape, 601 F.3d 743, 747 (7th Cir. 2010), citing United States v. Higdon, 531 F.3d 561, 565 (7th Cir. 2008); United States v. Baines, 777 F.3d 959, 966 (7th Cir. 2015) *474(relying on both written and oral statements of reasons to find judge adequately addressed mitigation arguments).
In this case, the district court’s written statement of reasons makes clear that the court did consider Reed’s family circumstances argument. The statement of reasons acknowledges Reed’s children, describes Mrs. Reed’s disability, and recognizes that with Reed in prison, the family would suffer hardship and have no means of support. After discussing other mitigating factors, the statement explains that, in the sentencing judge’s mind, those considerations were outweighed by the seriousness and shamelessness of the offense and of the defendant’s conduct once caught, including his false attempts to lay all the blame on his co-defendants. From the written statement, we are satisfied that the court considered the argument in mitigation and rejected it, quite understandably in light of the powerful aggravating factors the judge highlighted. It would be easier to affirm the sentence if the judge had said that during the sentencing hearing itself. But we see no value in remanding for an oral repetition of what was said in writing.
The judgment of the district court is AFFIRMED.