OPINION
Defendant Jose Humberto Solano-Ro-sales (“Defendant” or “Solano-Rosales”) appeals from the sentence imposed by the district court following his plea to the charge of returning to the United States without authorization after removal following a felony offense, in violation of 8 U.S.C. § 1326(a) and (b)(1). For the reasons set forth below, we AFFIRM the sentence.
I.
BACKGROUND
A. Factual History
Defendant is a Mexican citizen without legal status in the United States. He entered this country for the first time in 1992, and the following year married Lore-ta Cruz, a United States citizen. Defendant and Cruz have two children together, but they are no longer married. Prior to the instant prosecution, in the more than two decades since his initial entrance into the United States, Defendant was removed from the country three times. He also pled guilty to charges of domestic violence against Cruz on three different occasions. Pursuant to Michigan law, his last domestic violence conviction, as a third offense, was a felony.
According to the presentence report, Defendant was first discovered by the Border Patrol in Holland, Michigan in 1994; he was released pending an immigration hearing with an order to show cause. Defendant did not appear at his immigration hearing, and the immigration judge ordered his deportation on November 7, 1995.
During this period, Defendant faced his first criminal charges. In July 1995 he pled guilty to misdemeanor domestic violence charges arising from an incident involving his wife. He was given a suspended sentence of thirty days in jail and twelve months of probation. His wife filed a second complaint of domestic abuse at the Holland Police Department in September of 1995; Defendant was arrested on the resulting charges on October 12, 1995, and pled guilty to a misdemeanor on November 29, 1995. For this charge, he was sentenced to fifteen days in jail and twelve months of probation.
*350As a result of the previously initiated proceedings in immigration court, Defendant was ordered to report for his deportation on March 24, 1997; he complied with the order and was deported by plane the following day. On April 13, 1997, just weeks after his first deportation, Defendant attempted to gain entry into the United States at Harlingen, Texas, by presenting a fraudulent alien-registration card, which he later confessed to having purchased in Chicago. He was refused admission, and subsequently illegally reentered the United States near Donna, Texas.
In May 2001, Defendant filed an application to adjust his status to that of a lawful permanent resident on the basis of his marriage to Cruz. The application was denied, the removal order was reinstated, and Defendant was again removed to Mexico on November 24, 2003. In April 2004, Defendant filed an application to reenter the United States; that application was denied by immigration authorities on June 2, 2005.
Despite the denial, Defendant apparently reentered the United States at some point because in April 2007, he pled guilty to a felony charge of Domestic Violence-Third Offense in Michigan state court for a third incident involving his wife. Immigration authorities took him into custody in June of 2007, and he was removed on July 20, 2007. Prior to this last removal, Defendant was informed that he was barred from entering the United States for a period of twenty years. In his interview with the Probation Office, Defendant reported that he returned to the United States within a few months of this last deportation.
In May 2013, immigration authorities in Grand Rapids, Michigan learned of Defendant’s unlawful presence in the United States from information provided by a tip line. Defendant was thereafter taken into custody, and with the filing of an indictment in June 2013, the instant federal prosecution was commenced.
B. Procedural History
Defendant was charged with returning to the United States without authorization after having been previously removed subsequent to conviction for a felony offense, in violation of 8 U.S.C. § 1326(a) and (b)(1). He pled guilty on July 1, 2013, without entering into a plea agreement. The presentence report initially prepared by the Probation Office calculated an offense level of 21 and a criminal history category of II, resulting in an advisory guidelines range of 41 to 51 months. This calculation was predicated on a “crime of violence” enhancement of sixteen levels, pursuant to U.S.S.G. § 2L1.2(b)(l)(A)(ii), based on Defendant’s prior state felony conviction for domestic violence. Defendant filed an objection to the enhancement, and the government conceded that neither the statute nor the Shepard documents were sufficient to establish that the conviction was for a “crime of violence” within § 2L1.2(b)(l)(A)(ii). See United States v. Bernal-Aveja, 414 F.3d 625, 626-27 (6th Cir.2005) (discussing § 2L1.2(b)(l)(A)(ii) and Shepard, v. United States, 544 U.S. 13, 125 S.Ct. 1254, 161 L.Ed.2d 205 (2005)). The district court sustained the objection and applied in its place a four-level enhancement under 2L1.2(b)(l)(D) for a prior felony conviction. The resulting guidelines range was 8 to 14 months.
The district court determined that an upward variance from the guidelines range was warranted and imposed a custodial sentence of 18 months. In its sentencing colloquy, which will be discussed in more detail below, the district court cited Defendant’s record of domestic violence and repeated illegal reentries, and discussed the sentencing goals of specific deterrence, *351protection of the public, and just punishment in supporting the upward variance. In addition, to create further specific deterrence, the district court imposed a three-year term of supervised release. Upon the court’s direct inquiry, defense counsel stated that Defendant had no legal objections to the sentence.
Defendant timely appealed, but due to delays resulting from his attorney’s withdrawal from the case, briefing was not completed until late October 2014. Meanwhile, Defendant completed his term of imprisonment and was removed to Mexico on September 23, 2014.
II.
DISCUSSION
Defendant raises two arguments on appeal. First, he lodges a procedural reasonableness challenge to the imposition of the supervised release term based on the district court’s failure to discuss a guidelines provision recommending against sentencing removable aliens to supervised release terms following their custodial sentence. Second, Defendant argues that the upward variance in his custodial sentence was substantively unreasonable.
A. Imposition of the Supervised Release Term
1. Standard of Review
We review a district court’s sentencing determination “ ‘under a deferential abuse-of-discretion standard,’ for reasonableness.” United States v. Bolds, 511 F.3d 568, 578 (6th Cir.2007) (quoting Gall v. United States, 552 U.S. 38, 41, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007)). This review has two components: procedural reasonableness and substantive reasonableness. Id.; Gall, 552 U.S. at 51, 128 S.Ct. 586. Defendant challenges the imposition of the three-year supervised release term as procedurally unreasonable.
Because Defendant did not object to the sentence upon inquiry from the district court, our review is further constrained by the plain error standard. United States v. Vonner, 516 F.3d 382, 385-86 (6th Cir.2008) (en banc). To show plain error, Defendant “must show (1) error (2) that was obvious or clear, (3) that affected [Defendant's substantial rights and (4) that affected the fairness, integrity, .or public reputation of the judicial proceedings.” (United States v. Wallace, 597 F.3d 794, 802 (6th Cir.2010) (citing Vonner, 516 F.3d at 386)).
2. Analysis
Defendant’s procedural challenge to the supervised release term is based on the district court’s failure to mention and discuss a relevant guidelines provision, U.S.S.G. § 5Dl.l(c). Essentially, he argues that the district court’s failure to discuss this provision deprived him of an adequate explanation of his sentence. “A district court necessarily abuses its sentencing discretion if it ‘commitfs] [a] significant procedural error, such as ... failing to adequately explain the chosen sentence.’” Bolds, 511 F.3d at 579 (quoting Gall, 552 U.S. at 51, 128 S.Ct. 586). The district court must provide an “articulation of the reasons [it] reached the sentence ultimately imposed.” United States v. Jackson, 408 F.3d 301, 305 (6th Cir.2005). This explanation should be sufficient “to allow for meaningful appellate review.” United States v. Trejo-Martinez, 481 F.3d 409, 412-13 (6th Cir.2007). An explanation is typically adequate if it addresses the factors from 18 U.S.C. § 3553(a) that are relevant to the district court’s sentencing decision, id. at 413, but simply listing the factors and various characteristics of the defendant, without explanation of how the *352factors affect the sentence imposed, is insufficient, Bolds, 511 F.3d at 580 (citing United States v. Cousins, 469 F.3d 572, 577 (6th Cir.2006)). Additionally, “when a defendant raises & particular argument in seeking a lower sentence, the record must reflect both that the district judge considered the defendant’s argument and that the judge explained the basis for rejecting it.” United States v. Jones, 489 F.3d 243, 251 (6th Cir.2007) (internal quotation marks omitted).
The statute governing the imposition of supervised release is 18 U.S.C. § 3583. Subsection (c) of that statute instructs a court to consider enumerated factors from § 3553(a) (the statute setting forth factors governing imposition of sentences) both “in determining whether to include a term of supervised release” and “in determining the length of the term and the conditions of supervised release.” § 3583(c). Among other factors, a court is instructed to consider the nature of the offense and the history and characteristics of the defendant, the need for deterrence, the need to protect the public, and pertinent guidelines provisions and policy statements issued by the Sentencing Commission. Id. (cross-referencing § 3553(a)(1), (a)(2)(B), (a)(2)(C), (a)(4), and (a)(5)). Procedural reasonableness requires that the district court duly consider the § 3583(c) factors. United States v. Presto, 498 F.3d 415, 418 (6th Cir.2007); see also United States v. Hayes, 445 F.3d 536, 537 (2d Cir.2006).
We have made clear that the requirement of an adequate' explanation applies to the district court’s determination to impose supervised release to the same extent that it applies to a determination regarding the length of a custodial term. United States v. Inman, 666 F.3d 1001 (6th Cir.2012) (per curiam) (vacating and remanding on plain error review where the record did not show the district court considered the § 3553(a) factors or explained its reasons for imposing supervised release or the length of the term selected); United States v. O’Georgia, 569 F.3d 281, 288-89 (6th Cir.2009) (vacating a supervised release term that was “summarily imposed without an adequate explanation”). Although a “single consideration of the sentencing factors” relevant to both custodial and supervised release terms is permissible, the district court’s discussion should “embrace[] both the incarceration sentence and the supervised release term.” Presto, 498 F.3d at 419.
At the sentencing hearing in the present case, the district court considered Defendant’s criminal and immigration record and concluded that supervised release was appropriate to achieve specific deterrence. The district court began by stating that “[t]he history of the defendant, while he has been in the United States, has demonstrated a total lack of regard both for the immigration laws of our country as well as state law involving domestic violence.” (R. 32, Sentencing Transcript, PGID 142.) The court noted Defendant’s three convictions for domestic violence, including one felony, and stated:
In addition to that, he is facing his fourth removal from the United States. He gets removed, he comes back, and he comes back very quickly. And has always done it that way. And I see nothing in this record, and I appreciate [defense counsel’s] argument that his children are older and perhaps they can do — go about their lives in the United States without his physical presence, but I see nothing in this record that would lead me to believe that the defendant is going to stay in his native country, and I don’t think he is going to stay in his native country long.
*353 (Id. at 142-43.) Turning to the § 3553(a) factors that it found relevant to this case, the district court heavily emphasized the sentencing factor of deterrence. The court explained that it believed specific deterrence of Defendant was a priority in this case because “[n]othing that any judge in this country has done has deterred him from illegal activity.” (Id. at 143.) Noting that Defendant “continually violates the immigration laws of our country,” the district court determined that in its judgment Defendant “is a high risk to re-offend.” (Id.) The district court then directly explained its decision to impose a term of supervised release:
And I regretfully, and I hope I’m wrong, but I agree with [the government], that there is nothing in this record that would indicate that [Defendant] is going to stay in his native country, that’s why I intend to place him on supervised release for a maximum term allowed, which is for three years. Hopefully that will provide some sort of deterrence. And if he comes back and is apprehended again, he will come back to this [c]ourt. I am not going to waive jurisdiction over this defendant should he be apprehended in some other district in this country, he will come back and see me, if I’m still herei
(Id. at 144.)
Defendant argues that the district court failed to adequately explain the imposition of the supervised release term because the court did not acknowledge or discuss U.S.S.G. § 5Dl.l(c). That provision states that a district court “ordinarily should not impose a term of supervised release in a case in which supervised release is not required by statute and the defendant is a deportable alien who likely will be deported after imprisonment.” U.S.S.G. § 5Dl.l(c). Additionally, comment 5 to the rule explains that “[i]f such a defendant illegally returns to the United States, the need to afford adequate deterrence and protect the public ordinarily is adequately served by a new prosecution.” U.S.S.G. § 5D1.1, comment (n.5). The same comment recognizes, however, that the sentencing goals may not be adequately served without supervised release in all cases. Thus it recommends that a court should “consider imposing a term of supervised release on such a defendant if the court determines it would provide an added measure of deterrence and protection based on the facts and circumstances of a particular case.” Id.
We conclude that the district court erred in failing to acknowledge the guidelines recommendation against supervised release embodied in § 5Dl.l(c) or discuss its decision to take a different course of action in Defendant’s case. The Supreme Court has instructed that district courts must begin their sentencing decision with the applicable guidelines range, which, “[a]s a matter of administration and to secure nationwide consistency!,] ... should be the starting point and the initial benchmark.” Gall v. United States, 552 U.S. 38, 49, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007). In effect, § 5Dl.l(c) creates a guidelines recommendation of no term of supervised release for deportable aliens like Defendant, applicable where the offense does not carry a mandatory term of supervised release. In order to enable meaningful appellate review of a district court’s choice to impose a term of supervised release contrary to the recommendation of § 5Dl.l(c), the district court’s explanation should directly address that section’s recommendation against supervised release and provide the court’s reasoning for taking a different course of *354action in the case before it.1 Accord United States v. Bautista-Villanueva, 546 Fed.Appx. 260 (4th Cir.2013) (remanding where record did not show that district court considered § 5Dl.l(c) and its relevant commentary in imposing supervised release). To be clear, it is not the failure to cite the guidelines section that is procedurally unreasonable, but the failure to acknowledge and address its substantive recommendation.
Although the district court erred in failing to acknowledge and discuss the guidelines recommendation against supervised release embodied in § 5Dl.l(c), Defendant’s appeal cannot succeed under plain error review because his substantial rights were not affected. “An error affects substantial rights when it ‘affect[s] the outcome of the district court proceedings.’ ” Inman, 666 F.3d at 1006 (quoting United States v. Olano, 507 U.S. 725, 734, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993)). Here, there is no reason to believe that the district court’s failure to expressly discuss § 5Dl.l(c) impacted the sentence. The district court’s explanation that the supervised release term was necessary to achieve specific deterrence in light of Defendant’s record of repeated illegal re-entries in fact closely matches the guidelines commentary acknowledging that in some cases involving deportable aliens a term of supervised release may be appropriate to provide “an added measure of deterrence and protection.” U.S.S.G. § 5D1.1, comment (n.5). Had the district court directly discussed § 5Dl.l(c), it undoubtedly would have invoked the applicable language from comment 5 and engaged in substantively identical reasoning to what it in fact stated.
Defendant argues that “[t]he record is devoid of any facts pointed to by the district court that would show an enhanced need for deterrence or protection in this case.” Def.’s Br. at 8. This is plainly not the case. The district court pointed to Defendant’s pattern of rapidly returning each time he was removed from the country. The district court also pointed to the combination of Defendant’s immigration record and criminal history to support its conclusion that Defendant had shown no respect for the law, and that the actions of previous judges had not been sufficient to deter him. The district court stated that it hoped the supervised release term would “provide some sort of deterrence.” This explanation was adequate. Compare United States v. Espericueta-Perez, 528 Fed.Appx. 572, 576-78 (6th Cir.2013) (affirming supervised release term in similar circumstances where court pointed to the defendant’s “troubling” criminal history and previous “expeditious! ]” return to the country after incarceration and removal to conclude that defendant was not “easily deterred”); United States v. BecerriTrPena, 714 F.3d 347, 351 (5th Cir.2013) (affirming imposition of supervised release in § 5Dl.l(c) case where district court “supplied a sufficiently ‘particularized explanation’ of its decision” focusing on the defendant’s criminal history).
*355In sum, the district court’s discussion of the heightened need for specific deterrence in this case, and its reasoning as to how supervised release would further that goal, was explicit, grounded in the record, and clearly articulated. Bolds, 511 F.3d at 580 (requiring “an articulation of the reasons [the district court] reached the sentence[] imposed”). Additionally, the district court acknowledged defense counsel’s argument that Defendant was less likely to risk returning to the United States now that his children were older, but it reasonably determined based on his record of disregarding immigration law that Defendant was likely to attempt to return. See Jones, 489 F.3d at 251 (holding that the record must reflect that the district court considered defendant’s argument against the imposed sentence and explained the basis for rejecting that argument).
Because Defendant’s substantial rights were not affected by the court’s error in failing to directly acknowledge and discuss § 5Dl.l(c), we affirm the term of supervised release imposed by the district court.
B. Substantial Reasonableness of the Upward Variance 1. Mootness
At the outset, we must address the government’s argument that Defendant’s appeal of his custodial sentence is moot, in light of the fact that he completed his term of imprisonment on September 23, 2014 and was removed to Mexico the same day. “ ‘A federal court has no authority to render a decision upon moot questions or to declare rules of law that cannot affect the matter at issue.’ ” United States v. City of Detroit, 401 F.3d 448, 450 (6th Cir.2005) (quoting Cleveland Branch, N.A.A.C.P. v. City of Parma, 263 F.3d 513, 530 (6th Cir.2001)). To present a live case or controversy, Defendant must have, and continue to have throughout the litigation, “ ‘an actual injury traceable to the [government] and likely to be redressed by a favorable judicial decision.’ ” Spencer v. Kemna, 523 U.S. 1, 7, 118 S.Ct. 978, 140 L.Ed.2d 43 (1998) (quoting Lewis v. Continental Bank Corp., 494 U.S. 472, 477, 110 S.Ct. 1249, 108 L.Ed.2d 400 (1990)).
Where a criminal defendant challenges a completed custodial portion of his or her sentence while serving a subsequent term of supervised release, this Court has held that the appeal is not moot “so long as the appeal potentially implicates the length of the appellant’s supervised release term.” United States v. Maken, 510 F.3d 654, 656 n. 3 (6th Cir.2007) (internal quotation marks omitted). In practice, this means that a completed custodial sentence may be appealed so long as the district court would retain the discretion to reduce the sentence of supervised release on remand. United States v. Genschow, 645 F.3d 803, 813 (6th Cir.2011) (finding case not moot because district court had discretion to reduce or eliminate supervised release); United States v. May, 568 F.3d 597, 602 (6th Cir.2009) (“Because on any remand, the district court would be free to reduce May’s term of supervised release from three to two years, we hold that none of May’s issues on appeal are moot.”); see also United States v. Bravo, 362 Fed.Appx. 456, 459 (6th Cir.2010) (“[S]uch appeals are not moot if there remains a possibility that the district court could modify any term of supervised release to which the appellant remains subject.”). Here, there is no minimum supervised release term and therefore the district court would retain the discretion to reduce or eliminate Defendant’s supervised release term. The appeal is therefore not moot.
2. Standard of Review
When reviewing the substantive reasonableness of the district court’s *356sentencing decision, we apply a deferential .abuse-of-discretion review. Bolds, 511 F.3d at 578 (citing Gall v. United States, 552 U.S. 38, 41, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007)). Unlike procedural reasonableness claims, an appeal arguing that a sentence is substantively unreasonable is not subject to plain error review for failure to object at the sentencing hearing. United States v. Penson, 526 F.3d 331, 337 (6th Cir.2008). No presumption of reasonableness applies to sentences that, like the one imposed on Defendant, are outside the guidelines range. United States v. Herrera-Zuniga, 571 F.3d 568, 582 (6th Cir.2009).
3. Analysis
A sentence is substantively reasonable if it is “proportionate to the seriousness of the circumstances of the offense and offender, and sufficient but not greater than necessary, to comply with the purposes of § 3553(a).” United States v. Vowell, 516 F.3d 503, 512 (6th Cir.2008) (quotation marks omitted). However, “a sentence may be substantively unreasonable where the district court ‘selects the sentence arbitrarily, bas[es] the sentence on impermissible factors, fail[s] to consider pertinent § 3553(a) factors, or giv[es] an unreasonable amount of weight to any pertinent factor.’ ” United States v. Moon, 513 F.3d 527, 543 (6th Cir.2008). “[A] major departure [from the guidelines range] should be supported by a more significant justification than a minor one.” Gall, 552 U.S. at 50, 128 S.Ct. 586.
The guidelines range in Defendant’s case was 8 to 14 months; the district court determined that an upward variance was appropriate and imposed a sentence of 18 months. In making the remarks summarized above with regard to the importance of specifically deterring Defendant, the district court was also discussing its reasons for imposing an above-guidelines custodial sentence. (R. 32 at 143 (“I intend to vary upward in this case because of the specific deterrence of this defendant.”).) This basis for an upward variance was reasonable in light of Defendant’s criminal record and immigration history, which supported the district court’s determination that previously efforts by state and immigration judges had failed to adequately deter Defendant from breaking the law.
The district court also cited two other sentencing goals: the need to protect the public, and the need to provide for just punishment. With regard to the need to protect the public, the district court stated that “[t]he citizens of the United States have a right to know who is in their country, and this defendant continually violates the immigration laws of our country. He, in the Court’s judgment, is a high risk to re-offend.” (R. 32 at 143.) Under the deferential standard, and particularly when read in light of Defendant’s record of domestic violence recidivism in the United States after prior removals from the country, this additional justification for an upward variance is not substantively unreasonable. Just prior to making this statement, the Court had observed that “[n]othing that any judge in this country has done has deterred him from illegal activity,” a remark that encompassed Defendant’s criminal record in addition to his immigration record.
The district court very briefly remarked that “just punishment, in the [c]ourt’s judgment, is not accomplished by an advisory guideline range sentence in this case.” This possibly stray comment does at first blush appear problematic. We have recognized that 8 U.S.C. § 1326 states a “ ‘ma-lum prohibitum,’ or public welfare offense,” which does not encompass any morally culpable intent. United States v. *357 Hussein, 675 F.2d 114, 115-16 (6th Cir.1982) (per curiam) (citing Morissette v. United States, 342 U.S. 246, 72 S.Ct. 240, 96 L.Ed. 288 (1952)). In this vein, Defendant argued below that his reason for returning to this country was to care for his children, who are American citizens.
While a malum prohibitum crime like illegal reentry under 8 U.S.C. § 1326 seems a poor fit for an upward variance on retributive grounds, we conclude that the district court’s allusion to just punishment did not render Defendant’s above-guidelines sentence substantively unreasonable here, for three reasons. First, the variance was a relatively minor one, only four additional months above the guidelines range, so the sentence does not suggest that the district court imputed some incongruous degree of moral culpability to Defendant. Second, just punishment was not the dominant factor cited by the court— specific deterrence was clearly, and reasonably, the district court’s overriding goal — again suggesting that the district court was not motivated by unwarranted or disproportionate retributive purposes. Thus, because the variance was small and supported by other more prominent sentencing goals, this Court need not measure the district court’s stray remark against the standard of a “more significant justification” that is required for “a major departure.” See Gall, 552 U.S. at 50, 128 S.Ct. 586. Third, and contrary to Defendant’s arguments, his was not a “mine run” illegal reentry case, but rather one involving a defendant with three prior convictions for domestic violence. The district court could have better phrased its decision as “promoting] respect for the law,” another element of § 3553(a)(2)(A), but its single comment that “just punishment” would not be served by a within-guidelines sentence, on this record, does not render Defendant’s 18-month sentence substantively unreasonable.
In sum, we believe that the district court did not abuse its discretion in applying the sentencing factors from § 3553(a). Defendant’s custodial sentence was not substantively unreasonable.
CONCLUSION
For the foregoing reasons, Defendant’s sentence is AFFIRMED in all respects.