Michael Dill was placed on supervised release after serving 10 years in federal prison for bank robbery. Twice now he has been sent back to prison for committing multiple violations of conditions of release, this latest time for 14 months. In this appeal from the second revocation of supervised release, Dill contends that the district judge erred by having decided irrevocably before the revocation hearing that he would impose a new term of at least 12 months in prison — the term Dill received after the first revocation — without first considering the applicable sentencing guidelines, his arguments in mitigation, or the pertinent factors under 18 U.S.C. § 3583(e)(3) and § 3553(a). We affirm. The judge had obviously prepared for the decision and had some strong views at the beginning of the hearing. We do *823not think, however, that the judge’s preparation and thought crossed the line into an irrevocable commitment such that his mind was closed to what happened in the hearing.
I. Factual and Procedural Background
From December 2000 through March 2001, Dill and a confederate robbed several Chicago-area banks of over $21,000. Dill was caught and pled guilty in federal court to two counts of bank robbery under 18 U.S.C. § 2113(a). He was sentenced in the Northern District of Illinois to ten years in prison followed by a three-year term of supervised release.
Dill was released from prison in April 2012, and his supervision was transferred to the Eastern District of Wisconsin. Within a year, he had relapsed on drugs and violated four conditions of his supervised release: He missed drug tests and counseling appointments, tested positive for morphine and marijuana, traveled outside the judicial district without permission, and failed to comply with location-monitoring requirements.
The district court convened a revocation hearing in June 2013 but did not revoke Dill’s supervised release, instead continuing the proceedings to give Dill “another chance” to comply with his conditions of supervised release. But the court also warned Dill that any future violation would result in a 15-month term of reimprisonment.
One month later Dill again tested positive, this time for opiates, and he admitted frequent use of heroin. The district court reconvened the revocation hearing and calculated a reimprisonment range of 8 to 14 months based on Dill’s Grade C violations and Category VI criminal history. See U.S.S.G. § 7B1.4(a). Dill explained that he had started using drags again after his release from prison as a way of coping with the deaths of his daughter and mother during his incarceration. But he emphasized his positive work history, stable residence, and ongoing support from his girlfriend, and he asked the court to impose a reimprisonment term of time served (36 days) plus a requirement of psychological counseling. The court, though, expressed skepticism that counseling — which had not worked before — would sufficiently deter Dill. Despite the earlier threat of a 15-month term, the court imposed a 12-month term of reimprisonment, along with an additional 18 months of supervised release. Dill did not appeal that decision.
Dill completed the new prison term. Just seven months after his release, Dill was before the district court again, having accrued five more violations of his supervised release. He had: missed eight random drag tests and two counseling sessions; tested positive for morphine, codeine, and cocaine; committed two traffic violations; failed to notify his probation officer after contact with law enforcement; and failed to make regular restitution payments. Dill’s attorney submitted a letter asking the court to continue Dill’s supervision, again emphasizing his positive employment history and stable romantic relationship and describing Dill’s efforts at combatting his addiction. The court rejected Dill’s request for continued supervision. The district judge acknowledged that “addiction is perhaps central to the problem here” but added:
most offenders, including those with addiction, at some point, particularly after having spent the length of time that [Dill] did in prison, find it in their heart and in their outlook to put this aspect of their life behind [them], and take advantage of all of the programming and counseling that’s available.
*824When offenders choose not to conform their conduct to the law, the court continued, “there is only one alternative, and that is — because we, as a society, cannot have individuals in our midst who are either in a workplace, or in a home environment, or worse yet behind the wheel [of] a vehicle, high on drugs.” So, the court concluded, there was “no other alternative for Michael Dill anymore, other than to send [him] back to prison.”
The district court next turned to the length of that term of reimprisonment. Though the court recognized that the policy statements in Chapter 7 of the Sentencing Guidelines called for 8 to 14 months, the court explained that Dill’s term was “not going to be a year, and it’s not going to be two years,” but instead would “probably” be “something in-between” because, the court reasoned, “when you violate the conditions of supervised release, the penalties get ratcheted up.” The court thus rejected the government’s recommendation for 8 to 12 months and the defendant’s request for 6 months, emphasizing that Dill’s drug use made him a danger to society. And, the court repeated, its “options” were to impose a term “of not less than a year, and no more than two years.” The court concluded that a 14-month term of reimprisonment was the “only fair, just, and reasonable sentence.”
After the district court imposed a prison term of that length, the prosecutor asked the court to clarify whether it had considered the mitigating arguments from defense counsel’s letter and whether the court understood that the term could be less than 12 months, given the advisory range of 8 to 14 months. The court responded that the Sentencing Guidelines “were never mandatory in supervised release revocation proceedings.” The judge added:
I’m not going to reimpose a lower or same sentence that didn’t work the first time. In other words, the consequences are greater. And so they weren’t as great as perhaps they could have been, because I could have imposed a sentence of 24 months. In fact, some might suggest that that should have been the sentence.
The judge next turned to Dill’s arguments in mitigation. Though he had considered those arguments, the judge said, he was not persuaded to impose a shorter prison term:
[I]t was very clear at the' outset, we’ve been through this once with Mr. Dill. It didn’t work, and there are consequences. As I stated earlier, if this were Mr. Dill’s first revocation proceeding, it might be different. But it wasn’t. So as they say, it is what it is. And we can’t turn back the hands of mother time, nor put the genie back in the bottle. And Mr. Dill has no one to look to other than himself. And for an individual with the significant criminal history and the significant prior terms of imprisonment, including a 12 month sentence on supervised release, it ill behooves either [him] or anyone on his behalf to suggest that we set these violations aside and put him back on the street. That would be a total dereliction of any judicial officer’s responsibilities in enforcing and ensuring an appropriate, fair, just, and reasonable disposition.
Dill did not object to any aspect of the revocation proceeding.
II. Analysis
Few duties of a United States District Judge are as challenging or involve so much discretion as sentencing. At least where statutory mandatory minimum sentences do not dictate a decision, the Sentencing Guidelines and the key statutes on *825sentencing direct the judge to try to balance conflicting goals of sentencing. See 18 U.S.C. §§ 3553(a) & 3583(e)(3). The final decision cannot be reduced to a formula. The judge must exercise judgment about the individual case that is often not fully explainable in terms of deductive logic.
Dill’s appeal here is aimed at one of the inherent tensions in sentencing. The judge must prepare for a sentencing decision by reviewing the facts of the offense or violation and the history and characteristics of the offender and by considering the available choices. Rarely does a judge walk into a sentencing hearing without a fairly clear idea of an appropriate sentence. At the same time, the sentencing hearing itself is an essential step. Judges must keep their minds open to new facts, new arguments, and new choices. .
If the judge communicates those preliminary thoughts about an appropriate sentence to counsel near the beginning of the hearing, it can often help counsel and the defendant know what the judge is most concerned about and address their arguments to those points. On the other hand, if the judge is not careful with the language used, then counsel and the parties and a reviewing court can get the impression that the judge’s mind was already made up no matter what might happen in the sentencing hearing.
Dill’s sole contention on appeal is that the district court failed to maintain this balance in his case by refusing improperly to consider a second reimprisonment term below 12 months, the term he had received after his first revocation. Dill points to the court’s statement at the beginning of the hearing — that the court was considering a term between 12 and 24 months — as evidence that a term of at least 12 months had been decided in advance.
As Dill points out, we have cautioned district judges not to predetermine the appropriate punishment before convening a revocation hearing. See United States v. Smith, 770 F.3d 653, 655 (7th Cir.2014); United States v. Tatum, 760 F.3d 696, 697 (7th Cir.2014). District judges must approach revocation and sentencing hearings with an open mind and consider the evidence and arguments presented before imposing punishment. See United States v. Pulley, 601 F.3d 660, 665 (7th Cir.2010); United States v. Pless, 982 F.2d 1118, 1129 (7th Cir.1992).
At the same time, a judge who begins the hearing without any preliminary idea of appropriate sanctions is probably not prepared. Having such an idea does not disable the judge from making the sentencing decision. See Pulley, 601 F.3d at 665; Pless, 982 F.2d at 1129-30; see also Fleenor v. Farley, 47 F.Supp.2d 1021, 1052-53 (S.D.Ind.1998) (sentencing judge’s statement to counsel at start of hearing that he was leaning toward imposing death sentence meant that judge was prepared, not that he had made up his mind unalterably), aff'd, 171 F.3d 1096 (7th Cir.1999).
Taken in isolation, some of the district judge’s statements here could be read to suggest that he did not come into the hearing with an open mind, including his statement that the court’s “options” for Dill’s punishment were a term “of not less than a year, and no more than two years.” The judge also used some language that could be read as minimizing the discretion he actually had, saying “there is no other way,” referring to the sentence he was “obliged” to impose, and saying that the sentence imposed was “the only fair, just, and reasonable sentence.” Such language of necessity is not literally true but should not be understood literally. A judge pro*826nouncing sentence often explains to a defendant how the defendant has earned the sentence by his own choices, which have forced the judge to impose a just punishment. Such language does not mean that the judge has not given thoughtful consideration to the decision.1
The final decision must be made and announced in the hearing itself. Explanations are more often extemporaneous than carefully scripted. Explanations seek to weigh what cannot be measured and to balance competing goals as difficult as squaring a circle. For all these reasons, we must “be careful when a judge has made a spontaneous sentencing statement not to impose an unrealistically literal interpretation on his words.” Tatum, 760 F.3d at 697.
From the record as a whole, it is evident that the judge gave careful and individual consideration to Dill’s case. He did not “disable himself’ from considering a lower term before hearing all of the relevant information. See id.; Smith, 770 F.3d at 655 (reasoning that district court had not committed itself in advance to punishment announced by predecessor but instead had properly considered previous revocation in determining appropriate term of reimprisonment); United States v. Keatings, 787 F.3d 1197, 1204 (8th Cir.2015) (concluding that district court had considered § 3553(a) factors and did not confine itself to earlier threat of 10-year prison term).
The district judge announced at the start of the hearing that he would “probably” impose a term of reimprisonment between one and two years in light of the previous revocation. See Smith, 770 F.3d at 655 (explaining that fact of previous revocations was “something the judge was free, maybe required, to consider” in revocation proceedings). Before announcing the 14-month term, the judge acknowledged the Chapter 7 policy statements and assessed Dill’s new violations and the danger he posed to society. See United States v. Phillips, 791 F.3d 698, 702 (7th Cir.2015) (explaining that district court must justify term of reimprisonment “in light of the statutory sentencing factors and any relevant policy statements in the guidelines”); Tatum, 760 F.3d at 697 (instructing sentencing courts to consider “number and gravity” of supervised-release violations before determining whether to revoke supervision).
The general principle that the judge applied here, that he would not impose a lighter sentence for a second set of comparable violations, is both understandable and reasonable.. Yet the judge clearly made an individualized decision, taking into account Dill’s conduct both recent and remote, and his history and characteristics, including his long-term drug addiction. The judge wisely chose not to impose a new round of supervised release after this latest prison term.
Moreover, the judge had shown his flexibility by previously imposing a 12-month *827term of reimprisonment despite having warned Dill that another violation would produce a 15-month term. The judge was not so committed to a sentence of over 12 months, regardless of Dill’s arguments at the hearing, that the judge could not preside fairly over the revocation.
AFFIRMED.