SELYA, Circuit Judge.

Sentencing courts have broad discretion in setting conditions of supervised release — but broad discretion is not unbridled discretion. Defendant-appellant Jorge Mercado complains that the sentencing court went too far in this case and acted arbitrarily in setting the conditions of his supervised release. Concluding that the defendant's jeremiad is unconvincing, we affirm his sentence.

I. BACKGROUND

The defendant pleaded guilty to one count of failure to register under the Sex Offender Registration and Notification Act (SORNA), 18 U.S.C. § 2250(a). The SORNA registration requirement applied due to the defendant's interstate travel following a state-court conviction in 2002 for indecent assault arising out of the rape of a 15-year-old girl. The defendant was 31 years old at the time of the offense.

At sentencing, the district court set the guideline sentencing range at 30 to 37 months, based in part on a criminal history category of VI (the highest available). In the process, the court observed that the defendant had what may have been one of the most profuse criminal histories the court had ever seen. This history spanned a period of more than 20 years and included over 45 infractions running the gamut from drug offenses to property crimes to violent crimes (such as domestic assault and domestic battery). Additionally, the court noted that while awaiting trial, the defendant had repeatedly violated the terms of his pretrial release. These violations included, among other things, continuing to fail to register under SORNA, failing to appear in state court following an arrest for driving without a license, testing positive for cocaine use, and no fewer than ten instances of failing to comply with location restrictions.

When all was said and done, the district court imposed a top-of-the-range incarcerative sentence of 37 months, to be followed by a five-year term of supervised release. The court explained that the sentence was driven by three salient considerations: the nature of the offense, the defendant's criminal history, and the defendant's "egregious" non-compliance with the terms of his pretrial release. The court ascribed particular importance to supervised release, spinning a web of special conditions, see USSG § 5D1.3(d), and suggesting that if the defendant complied with the supervised release terms, he might have a chance to break the "cycle of crime" that characterized his adult life.1

Among the special conditions imposed by the court, four are challenged on appeal. One such condition requires the defendant to participate in a sex-offender treatment program "as directed by the probation officer" and to submit to periodic polygraph testing at the probation officer's discretion to ensure compliance. The remaining three conditions circumscribe the defendant's contact with minors in various ways. One forbids the defendant from having any contact with a child under the age of 18 without the prior approval of the probation officer and the presence of an approved adult who is aware of the defendant's criminal history. Another prohibits the defendant from living with a child under the age of 18 unless the probation officer first approves. The last condition bars the defendant from working or volunteering in any situation in which there is access to children unless authorized in advance by the probation officer.

The defendant argued at sentencing that none of these conditions was supported by the record and that his lone conviction for a sex offense was irrelevant because it occurred more than ten years earlier. In the defendant's view, his more recent malefactions did not justify a conclusion that he presented a danger to children (or anyone else, for that matter). The district court overruled the defendant's objections. With respect to the sex-offender treatment condition, it stated:

With respect to the remaining three conditions, the court stated:

This timely appeal ensued.

II. ANALYSIS

We divide our analysis into two segments. The first segment deals with the sex-offender treatment condition. The second segment deals with the balance of the challenged conditions.

A. The Sex-Offender Treatment Condition.

The defendant challenges the imposition of the sex-offender treatment condition and related polygraph testing on two grounds. Neither ground is persuasive.

1. Delegation. We start with the defendant's claim that the sex-offender treatment condition constitutes an unlawful delegation of the district court's sentencing authority. In support, the defendant points to the district court's statements that sex-offender treatment is to be "as directed by the Probation Office" and that the "Probation Office has the discretion to require" the defendant to attend treatment sessions. These statements, the defendant says, show that the court granted "unfettered discretion" to the probation office. That grant, the defendant says, is unconstitutional.

There is a procedural obstacle to this claim of error: it is raised for the first time in this court. Consequently, it is subject only to review for plain error. See United States v. Padilla, 415 F.3d 211, 218, 220 (1st Cir.2005) (en banc); see also United States v. Bey, 188 F.3d 1, 10 (1st Cir.1999) (applying plain error review where defendant's objections were on grounds different than those raised on appeal).

Plain error review engenders a four-part inquiry. The appellant must show "(1) that an error occurred (2) which was clear or obvious and which not only (3) affected the defendant's substantial rights, but also (4) seriously impaired the fairness, integrity, or public reputation of judicial proceedings." United States v. Duarte, 246 F.3d 56, 60 (1st Cir.2001).

We need not tarry. This case does not require us to make a definitive ruling on the lawfulness of the delegation. Even assuming, for argument's sake, that the delegation is improper, and that the error is clear, the defendant cannot satisfy either of the last two parts of the plain error test.

We do not write on a pristine page. In the past, we twice have rejected, under plain error review, unpreserved delegation challenges to supervised release conditions. See United States v. Sánchez-Berríos, 424 F.3d 65, 81-82 (1st Cir.2005); Padilla, 415 F.3d at 220-21. Although those decisions did not involve sex-offender treatment, they are nonetheless instructive here.

We go directly to the third prong of plain error review. In assessing whether an unlawful delegation of sentencing authority affects a defendant's substantial rights, we must gauge whether he has shown a reasonable probability that, but for the alleged error, the court would likely have imposed a different and more favorable sentence. See Padilla, 415 F.3d at 221. When the challenged delegation grants the probation officer the discretion to require, in the first instance, that the defendant undergo some sort of treatment or testing, the plain error test places the defendant in the "nearly impossible" position of proving two variables. Id. First, he must show a fair probability that the court, acting directly, would not have mandated such treatment or testing. Second, he must show that the probation officer will likely exercise her discretion to require the defendant to participate in such treatment or testing. See id. The uncertainties surrounding those questions erect too high a hurdle for the defendant to clear.

Even if the defendant could show that the district court, delegation aside, would not itself have imposed the sex-offender treatment condition — a proposition that, on this record, verges on wishful thinking — there is simply no way that the defendant can show that, upon his future release from incarceration, the probation officer is likely to require him to participate in sex-offender treatment. It follows inexorably that the defendant cannot show that the sentencing outcome would have been more favorable to him had the alleged delegation error not occurred and, thus, the delegation did not affect the defendant's substantial rights. See Sánchez-Berríos, 424 F.3d at 81-82; Padilla, 415 F.3d at 221.

The fourth prong of the plain error test is equally inhospitable to the defendant's claim: the alleged delegation error does not in any way undermine the fairness, integrity, or public reputation of the sentencing proceeding. Where, as here, supervised release will not commence until the end of a substantial term of immurement, most people would think it both fair and sensible to postpone the decision as to whether sex-offender treatment is needed until the commencement of supervised release. That is precisely what the district court's delegation accomplishes. And in any event, we have held before that delegation errors concerning matters incidental to a defendant's sentence are not so "grave or consequential" as to demand resentencing under plain error review. Padilla, 415 F.3d at 221-22. That reasoning applies here.

We add that the defendant is not without recourse should the probation officer abuse the discretion delegated to her. A district court may at any time prior to the conclusion of a supervised release term "modify, reduce, or enlarge the conditions of supervised release." 18 U.S.C. § 3583(e)(2); see Fed.R.Crim.P. 32.1 advisory committee's note (explaining that in event of "unreasonableness on the part of the probation officer, the probationer should have recourse to the sentencing court when a condition needs clarification or modification"). If future developments indicate that the probation officer is attempting unreasonably or unnecessarily to require sex-offender treatment, the defendant may move the district court for relief.

To say more about the delegation argument would be supererogatory. Suffice it to say that we discern no plain error in the court's grant of discretion to the probation officer with respect to the defendant's possible participation in sex-offender treatment.

2. Reasonableness. This brings us to the defendant's attack on the reasonableness of the sex-offender treatment condition. Refined to bare essence, the defendant argues that supervised release is intended primarily to serve rehabilitative ends and the sex-offender treatment condition fails to serve those ends; that the district court did not provide a sufficient justification for imposing the condition; and that the condition is an unwarranted deprivation of liberty, unsupported by the record. Since this claim of error was preserved below, our review is for abuse of discretion. See United States v. Smith, 436 F.3d 307, 310 (1st Cir.2006); United States v. York, 357 F.3d 14, 19 (1st Cir. 2004).

We begin with first principles. A sentencing court is authorized to impose any condition of supervised release that is reasonably related to one or more of the permissible goals of sentencing. See 18 U.S.C. § 3583(d)(1) (cross-referencing 18 U.S.C. § 3553(a)(1) and (a)(2)(B) through (D)); see also United States v. Prochner, 417 F.3d 54, 63 (1st Cir.2005); USSG § 5D1.3(b)(1). These goals include deterrence, rehabilitation, and protection of the public. See 18 U.S.C. § 3583(d)(1). The risk of recidivism among convicted sex offenders is "frightening and high," McKune v. Lile, 536 U.S. 24, 33, 122 S.Ct. 2017, 153 L.Ed.2d 47 (2002), and sex-offender treatment has been linked to reduced recidivism, see United States v. Morales-Cruz, 712 F.3d 71, 75 (1st Cir.2013); York, 357 F.3d at 21. In light of the defendant's prior conviction for a sex offense against a minor and his prodigious criminal history, we think it apparent that a sex-offender treatment condition is reasonably related to rehabilitation and protecting the public.

The defendant's second point is no more telling. The district court made pellucid that the supervised release term was designed not only to help the defendant in abating his criminal tendencies but also to curtail future registration violations. This is a shorthand for saying that the condition was designed to court's design was consistent with these goals and, in the bargain, promoted public safety. It is, therefore, nose-on-the-face plain that the court's sentencing rationale was both plausible and sufficient to ground the imposition of a sex-offender treatment condition. See Morales-Cruz, 712 F.3d at 75; York, 357 F.3d at 21.

The defendant's last attack on the reasonableness of the sex-offender treatment condition is easily repulsed. We agree with the defendant that a failure to register under SORNA is not itself a sex offense. See USSG § 5D1.2, comment. (n.1). Contrary to the defendant's importunings, however, sex-offender treatment may be imposed as a condition of supervised release even when the offense of conviction is not itself a sex offense. See, e.g., Morales-Cruz, 712 F.3d at 72, 75; United States v. Sebastian, 612 F.3d 47, 48, 50-51 (1st Cir.2010); York, 357 F.3d at 19-21.

The appropriateness of such a condition is evident here. After all, the defendant had been convicted of sexually assaulting a minor in the past. Even though that conviction occurred some ten years prior to sentencing in this case, the defendant's persistent criminal involvement over the intervening years makes his earlier offense highly relevant. See York, 357 F.3d at 20-21; United States v. Brown, 235 F.3d 2, 6 (1st Cir.2000). What is more, the justification for the sex-offender treatment condition is bolstered by the fact that the defendant continued to flout sex-offender registration requirements even during pretrial release. The sex-offender treatment condition is, therefore, reasonably related to the defendant's history and characteristics and is not an overly broad deprivation of liberty.2

B. The Remaining Conditions.

The defendant's challenge to the remaining conditions (all of which to some extent inhibit his interaction with minors) has three facets. He starts with the argument that the conditions do not serve the purposes identified by the district court. He adds that the conditions are overbroad and unrelated to either his history and characteristics or any legitimate sentencing objective. Finally, the defendant — noting that he has two minor children — argues that the conditions infringe upon his constitutional rights of freedom of association and familial association. These arguments are futile.

The sentencing court's rationale for imposing these conditions is clear-cut. The court stated unequivocally that compliance with the conditions would promote the defendant's rehabilitation. In addition, the conditions were intended to mitigate the obvious risk of recidivism by requiring the defendant to obtain the probation officer's approval before coming into contact with minors. With this tableau in mind, we have no difficulty in concluding that the district court's rationale is plausible.

The defendant's second argument is no more compelling. The conditions appear to draw heavily on the defendant's history and characteristics and are buttressed by case-specific reasons. See United States v. Gilman, 478 F.3d 440, 446 (1st Cir.2007). For one thing, the defendant previously had been convicted of a sex offense against a minor. For another thing, the offense of conviction is a failure to register under SORNA — a type of lapse that has been credibly linked to an increased risk of recidivism. See Morales-Cruz, 712 F.3d at 75. These facts make manifest that the challenged conditions are reasonably related to the defendant's prior history and characteristics. See, e.g., United States v. Rodriguez, 558 F.3d 408, 411, 413-14 (5th Cir.2009).

In an effort to show that the court mechanically applied cookie-cutter conditions, the defendant pounces upon the court's statement that these conditions are "fairly standard in sex offender cases." But the defendant wrests that statement from its contextual moorings: the court did not stop there but, rather, went on to explain that these conditions were intended to mitigate the risk of this particular defendant re-offending. To seal the deal, the court specifically linked the rehabilitative and deterrent features of the supervised release term and its conditions to the defendant's lengthy criminal history and his persistent failure to comply with the terms of his pretrial release.

The defendant's third argument has a patina of plausibility. Supervised release conditions that unduly restrict a defendant's contact with his own minor children may spark concerns related to the constitutional right of familial association.3 See, e.g., United States v. Worley, 685 F.3d 404, 408 (4th Cir.2012); United States v. Lonjose, 663 F.3d 1292, 1303 (10th Cir. 2011); United States v. Loy, 237 F.3d 251, 269-70 (3d Cir.2001). Here, however, the conditions are sufficiently circumscribed so that no such concerns arise.

Importantly, the conditions imposed by the district court do not comprise an out-right ban on the defendant's ability to associate (or even live) with his minor children. They merely require that his association with his children be pre-approved by the probation officer and take place in the presence of an adult familiar with his criminal history. There is no basis for believing that the probation officer will unreasonably withhold permission for the defendant to see his own children. If she does, the defendant has an easily available avenue for redress. See 18 U.S.C. § 3583(e)(2); Fed.R.Crim.P. 32.1 advisory committee's note.

That ends this aspect of the matter. The group of supervised release conditions restricting the defendant's interactions with minors do not impress upon the defendant a greater deprivation of liberty than is reasonably necessary to serve the goal of deterrence. See, e.g., United States v. Tang, 718 F.3d 476, 487 (5th Cir.2013) (per curiam); United States v. Roy, 438 F.3d 140, 144-45 (1st Cir.2006). Thus, the district court did not act outside the commodious encincture of its discretion in imposing these conditions.

III. CONCLUSION

We need go no further. For the reasons elucidated above, we uphold the challenged conditions of supervised release.

Affirmed.