¶ 1. The DNA surcharge topic that we address in this case applies to a defendant who committed crimes before the effective date of a relatively new DNA surcharge statute, but was sentenced after that date. Because this defendant, Gregory Radaj, was convicted of four felonies, his DNA surcharge was higher than it would have been under the law in effect at the time he committed his crimes. As most pertinent to our analysis, the revised statute provides for a mandatory surcharge in the amount of $250 per felony conviction. See Wis. Stat. § 973.046(lr)(a).1 Consequently, Radaj’s DNA surcharge was $1,000, rather than a discretionary $250 amount, the amount that it would have been under the prior law. Radaj argues that the new DNA surcharge statute as applied to him is an unconstitutional ex post facto law. We agree. We reverse on the DNA surcharge issue and remand for further proceedings, consistent with our decision.
Discussion
¶ 2. Radaj was charged with 21 misdemeanors and felonies relating to Radaj entering and taking items from motor homes on January 28, 2013. For purposes of the issue on appeal, the particulars of these crimes do not matter. What does matter is the *637number of crimes, when they were committed, and the timing of Radaj's sentencing.
¶ 3. As noted, Radaj committed his crimes on January 28, 2013. Pursuant to a plea agreement, Radaj was convicted of four felonies and was sentenced on March 26, 2014. The four convictions and those two dates set the scene for Radaj's ex post facto challenge to a new DNA surcharge statute that became effective between the time Radaj committed his crimes and the time he was sentenced.
¶ 4. The new DNA surcharge statute is more onerous, and applies to all defendants sentenced on or after the effective date of the new statute, January 1, 2014, even if they, like Radaj, committed their crimes before that date. See 2013 Wis. Act 20, §§ 2355, 9426(l)(am).
¶ 5. Under the prior law, Radaj would have been subject to a discretionary $250 DNA surcharge. See Wis. Stat. § 973.046(lg) (2011-12). Under the new law, given the number of Radaj's felony convictions, there was a mandatory $1,000 DNA surcharge (four felonies x $250). See Wis. Stat. § 973.046(lr)(a). According to Radaj, this means that the punishment for his crimes was increased after he committed those crimes, something that is prohibited by the ex post facto clauses in the federal and state constitutions.2 As we shall see, this ex post facto question turns on *638whether the DNA surcharge statute, as applied to Radaj, was a punitive criminal statute or a non-punitive civil statute.
¶ 6. Our discussion proceeds in four parts below. First, we briefly describe the new DNA surcharge statute and related statutes. Second, we summarize relevant ex post facto standards. Third, we apply those standards to Radaj and conclude that he has shown an "as applied" constitutional violation. Fourth, we address remedy.
¶ 7. We pause here to stress two apparent limitations on the applicability of our discussion to other defendants. First, it is important to our analysis that Radaj was convicted of multiple crimes and, therefore, the surcharge increased with each conviction. We do not resolve whether there is an ex post facto problem if all of the facts were the same except that Radaj had been convicted of a single crime. Second, there obviously is no ex post facto problem in applying the DNA surcharge statute to criminal defendants on a going-forward basis. That is, had Radaj committed his crimes after the DNA surcharge statute's effective date, he obviously could not assert an ex post facto violation, regardless whether the surcharge is punitive.
A. The Statutory Scheme
¶ 8. Under the law in effect at the time Radaj committed his crimes, if a court imposed a felony sentence or placed a person on probation, the court could, in its discretion, impose a DNA surcharge in the amount of $250, unless an underlying conviction was for a specified sex crime, in which case the surcharge was mandatory. See Wis. Stat. § 973.046(lg) and (lr) *639(2011-12). The surcharge amount, if imposed, was $250, regardless of the number or nature of the convictions.3 See id.
¶ 9. After Radaj committed his crimes but before he was sentenced, the revised DNA surcharge statute took effect. Under the new statute, if a court imposes a sentence or places a person on probation, the court must impose a DNA surcharge. That surcharge is calculated by adding together $250 per felony conviction and $200 per misdemeanor conviction. See Wis. Stat. § 973.046(lr).4
¶ 10. Before and after the revision, related statutes shed light on how the DNA surcharge is to be used. Before, if a court imposed a sentence or placed a person on probation for a felony or other specified crime, the court had to require the person to provide a biological specimen to the state crime laboratories for analysis. Wis. Stat. § 973.047(lf) (2011-12). Now, a court imposing a sentence or placing a person on probation for any crime must require the person to provide a biological specimen to the state crime labo*640ratories for analysis. See Wis. Stat. § 973.047(1f).5 All moneys collected from DNA surcharges must be "utilized under s. 165.77." Wis. Stat. § 973.046(3); Wis. Stat. § 973.046(3) (2011-12). Wisconsin Stat. § 165.77 governs Wisconsin's DNA data bank, which is administered by the Wisconsin Department of Justice. See Wis. Stat. § 165.77(8); Wis. Stat. § 165.77(8) (2011-12). Permissible DNA-analysis-related activities under § 165.77 include analyzing DNA samples collected from convicted criminal defendants, analyzing DNA samples collected as part of law enforcement investigations, and comparing the DNA profiles from such samples as allowed by statute. See § 165.77(2)(a)1.a. and 2. and (3); § 165.77(2)(a)1.a. and 2. and (3) (2011-12). Thus, the legislature has directed that DNA surcharges be used for these DNA-analysis-related activities.
B. Standards For Ex Post Facto Challenge
¶ 11. Radaj does not argue that the DNA surcharge statute is unconstitutional in all of its applications; his is not a facial challenge. Rather, Radaj contends that the new surcharge statute as applied to him is an unconstitutional ex post facto law. Radaj *641argues that, under his particular circumstances, the legislature increased the punishment for his crimes after he committed them. The burden of showing unconstitutionality is on Radaj. See State v. Thiel, 188 Wis. 2d 695, 706, 524 N.W.2d 641 (1994).
¶ 12. As pertinent here, an ex post facto violation occurs if a law "inflicts a greater punishment than the law annexed to the crime at the time it was committed." Id. at 701 (quoted source and internal quotation marks omitted). The retroactive nature of the new DNA surcharge statute is not disputed. By its terms, that statute applies to all sentencings even when, as here, the underlying crimes were committed before the law's effective date. There is also no dispute that, as applied to Radaj, the DNA surcharge that he was required to pay increased. The only disputed issue is whether the new surcharge statute, as applied to Radaj, "is a nonpunitive civil statute or a punitive criminal statute." See State v. Rachel, 2002 WI 81, ¶ 22, 254 Wis. 2d 215, 647 N.W.2d 762. Whether a statute is punitive for ex post facto purposes presents a question of law that we review de novo. Id., ¶ 23; City of South Milwaukee v. Kester, 2013 WI App 50, ¶ 21, 347 Wis. 2d 334, 830 N.W.2d 710, review denied, 2013 WI 87, 350 Wis. 2d 729, 838 N.W.2d 636.
¶ 13. In deciding whether a statute is punitive, courts apply a two-part "intent-effects" test. See Rachel, 254 Wis. 2d 215, ¶¶ 39-42; Kester, 347 Wis. 2d 334, ¶ 22. First, we ask whether the legislature's "intent" was to punish or rather was to impose a non-punitive regulatory scheme. See Kester, 347 Wis. 2d 334, ¶ 22. This intent inquiry is "primarily a matter of statutory construction that asks whether the *642legislative body[] ' . . . indicated either expressly or impliedly a preference for one label or the other.'" Id., ¶ 23 (quoted source omitted). If the legislature intended the law to be punitive, our inquiry ends. Id., ¶ 22. If the legislature intended a non-punitive regulatory scheme, then we proceed to the second "effects" part of the test. Id.
¶ 14. The "effects" inquiry asks whether, despite the fact that the legislature intended a non-punitive regulatory scheme, "the effects of the sanctions imposed by the law are 'so punitive ... as to render them criminal.'" Id. (quoted source omitted). "[0]nly the 'clearest proof will convince us that what a legislative body has labeled a civil remedy is, in effect, a criminal penalty." Id. (quoted source omitted). When determining whether a scheme is punitive in effect, we consider the following non-exhaustive list of factors:
(1) whether [the law in question] involves an affirmative disability or restraint; (2) whether it has historically been regarded as a punishment; (3) whether it comes into play only on a finding of scienter; (4) whether its operation will promote the traditional aims of punishment — retribution and deterrence; (5) whether the behavior to which [the law] applies is already a crime; (6) whether an alternative purpose to which it may rationally be connected is assignable for it; and (7) whether it appears excessive in relation to the alternative purpose assigned.
Rachel, 254 Wis. 2d 215, ¶ 43.
C. DNA Surcharge Statute As Applied To Radaj
¶ 15. Neither Radaj nor the State systematically applies the two-part intent-effects test. As we understand it, Radaj argues that several aspects of the *643surcharge, including, as most pertinent here, the per-conviction calculation, make the surcharge punitive. Both parties rely on case law from other jurisdictions. Some of this case law applies the intent-effects test. We discuss this case law within the framework of the intent-effects test.
1. Intent
¶ 16. As we explain below, we conclude that Radaj's ex post facto challenge succeeds because the DNA surcharge statute has a punitive "effect" as it applies to Radaj. This means that we need not resolve the "intent" part of the ex post facto test. Still, we choose to briefly discuss "intent," although we ultimately simply assume without deciding that the legislature intended a non-punitive regulatory scheme.
¶ 17. The legislature gave the DNA surcharge a civil label by calling it a "surcharge" instead of a fine. We give "great deference" to such labels. See Rachel, 254 Wis. 2d 215, ¶ 42.
¶ 18. In addition, the legislature's directive that DNA surcharges be used to defray costs of DNA-analysis-related activities under Wis. Stat. § 165.77 suggests that there was a legislative intent to implement a non-punitive regulatory scheme. Although the DNA-analysis-related activities relate to crime investigation, those activities seem distinct from punishment for the crimes underlying the DNA surcharge.
¶ 19. One of the "intent" cases that the State relies on most heavily, Eubanks v. South Carolina Department of Corrections (In re DNA Ex Post Facto Issues), 561 F.3d 294, 299-300 (4th Cir. 2009), persuasively underscores these points. In In re DNA, the *644Fourth Circuit Court of Appeals held that South Carolina's DNA "processing fee" was not intended to be punitive because it was a relatively small fee ($250) used to implement and maintain a DNA database:
The requirement that those providing the samples pay a $250 processing fee ... is not punitive in nature. The South Carolina General Assembly expressly provided that the funds generated by the fees will be "credited... to offset the expenses [the state law enforcement agency] incurs in carrying out the provisions of [the pertinent DNA database statute]." And, the relatively small size of the fee also indicates that it was not intended to have significant retributive or deterrent value. Thus, the "structure and design" of the statute demonstrate that the fee was intended to be an administrative charge to pay for the substantial expenditures that would be needed to implement, operate, and maintain the DNA database.
Id. (citations, footnote, and quoted source omitted; bracketed material added).
¶ 20. As the State points out, other courts have reached much the same conclusion when addressing a DNA surcharge in a similar amount that is used for similar purposes. See People v. Higgins, 13 N.E.3d 169, 176 (Ill. App. Ct. 2014) (citing People v. Guadarrama, 955 N.E.2d 615, 618 (Ill. App. Ct. 2011)); Commonwealth v. Derk, 895 A.2d 622, 625-30, 630 & n.6 (Pa. Super. Ct. 2006); see also State v. Brewster, 218 P.3d 249, 251 (Wash. Ct. App. 2009).
¶ 21. Were it not for the fact that Wisconsin's DNA surcharge increases with each conviction, unlike the surcharges in the above-cited cases, we might have little trouble concluding that the legislature had a non-punitive intent. However, as our "effect" discussion below suggests, the legislative decision to tie the *645amount of the surcharge to the number of convictions, something seemingly unrelated to the cost of the DNA-analysis-related activities that the surcharge funds, casts doubt on legislative intent. See Kester, 347 Wis. 2d 334, ¶ 23 (the intent inquiry asks whether "the legislative body[] ' . . . indicated either expressly or impliedly a preference for one label or the other'" (emphasis added; quoted source omitted).6
¶ 22. To repeat, we do not decide whether the legislature's intent was to punish or to impose a non-punitive regulatory scheme. Rather, assuming without deciding that the legislature's intent was non-punitive, we explain next that the new DNA surcharge statute is an ex post facto law as applied to Radaj because, as so applied, it has a punitive effect.
2. Effect
¶ 23. As already indicated, the parties do not systematically address the "effects" factors listed in Rachel. For the most part, it seems obvious that some of these non-exclusive factors cut in favor of Radaj and some factors cut in favor of the State. For example, under the fifth factor, the DNA surcharge applies to *646behavior that is already a crime, suggesting that the surcharge has the effect of punishing criminal behavior. See Rachel, 254 Wis. 2d 215, ¶ 43. On the other hand, under the first factor, the surcharge does not punish by imposing an affirmative restraint. See id.
¶ 24. In our view, the factors with the clearest relevance here, and those that are most heavily disputed by the parties, are the fourth, sixth, and seventh factors. The fourth factor is whether the DNA surcharge's "operation will promote the traditional aims of punishment," the sixth factor is whether the surcharge is "rationally. . . connected" to some non-punitive purpose, and the seventh factor is whether the surcharge "appears excessive in relation to" the non-punitive purpose the legislature assigned to it. See id.
¶ 25. As we see it, these three factors are closely related and of particular importance when, as here, a monetary amount intended to fund specified activities under a non-punitive regulatory scheme is at issue. When that is the situation, a critical inquiry is whether there is a rational connection between the amount of the fee and the non-punitive activities that the fee is intended to fund, or if instead the amount of the fee is excessive in relation to that purpose. If there is no rational connection and the fee is excessive in relation to the activities it is intended to fund, then the fee in effect serves as an additional criminal fine, that is, the fee is punitive.
¶ 26. In keeping with our observations regarding ex post facto analysis as it applies to fees, the case law cited by the parties reflects an emphasis on examining the amount of the surcharge or fee in question and asking whether there is a rational relationship between that amount and the non-punitive activities the *647surcharge or fee is intended to fund. In In re DNA, for example, the Fourth Circuit made a point of noting that the challenger "offer [ed] nothing to suggest that $250 is excessive considering the costs associated with the [DNA] database." In re DNA, 561 F.3d at 300.
¶ 27. In the case on which the State relies most extensively, Mueller v. Raemisch, 740 F.3d 1128 (7th Cir. 2014), the Seventh Circuit Court of Appeals focused on the rational connection between the amount of a fee and the costs the fee was intended to cover. See id. at 1133-35. That case involved Wisconsin's $100 annual sex offender registration fee. In holding that the fee was not punitive, the Mueller court considered the amount of the fee in light of a list of "formidable," ongoing tasks associated with the sex offender registry. See id. at 1133-34. The court concluded that there was no reason to think that the fee was unreasonable in relation to these tasks. Id. The court acknowledged that any fee "doubtless bears only an approximate relation to the cost it is meant to offset." Id. at 1133. However, "one basis for reclassifying a fee as a fine [and therefore punitive] would be that it bore no relation to the cost for which the fee was ostensibly intended to compensate." Id.
¶ 28. In contrast, and also in the context of an ex post facto challenge, the California Court of Appeal concluded that a DNA "penalty assessment" was punitive when it was assessed in an amount proportionate to the size of the defendant's criminal fine and, therefore, "in proportion to the defendant's criminal culpability." See People v. Batman, 71 Cal. Rptr. 3d 591, 592-94 (Cal. Ct. App. 2008). The Batman court contrasted such a proportionate penalty to other non-punitive fees that were "limited to the actual administrative costs." See id. at 593. Similarly, the Colorado *648Supreme Court concluded in an ex post facto challenge that Colorado's "drug offender surcharge" was punitive when the surcharge was "correlated to the degree of felony committed," rather than any apparent administrative costs. See People v. Stead, 845 P.2d 1156, 1157, 1160 (Colo. 1993).
¶ 29. Accordingly, we see the remaining question as whether, under Wisconsin's statutory scheme, there is some rational connection between calculating the DNA surcharge on a per-conviction basis and the cost of the DNA-analysis-related activities that the surcharge is meant to cover. We conclude that this per-conviction approach to setting the DNA surcharge makes the surcharge more like the punitive provisions in Batman and Stead than like the fixed DNA surcharges that other courts have held to be non-punitive.
¶ 30. As the Seventh Circuit in Mueller recognized, the connection between a surcharge and the costs it is intended to cover need not be perfect to be rational. Thus, we must give the legislature broad leeway to select a surcharge amount. But under the scheme at issue here, the legislature has imposed a multiplier that corresponds not to costs, but to the number of convictions. For this surcharge scheme to be non-punitive, there must be some reason why the cost of the DNA-analysis-related activities under Wis. Stat. §§ 973.046 and 165.77 increases with the number of convictions. We perceive no reason why this might be true. Taking Radaj as an example, suppose that, during plea negotiations, Radaj had somewhat more leverage and his plea agreement involved him entering pleas to two felonies, rather than four. If so, his DNA surcharge would have been $500, rather than $1,000. Or, suppose he had less leverage and entered pleas to *649eight felonies and four misdemeanors, making his DNA surcharge $2,800. In either case, there is no reason to think that the costs associated with analyzing Radaj's DNA sample and undertaking the other DNA-analysis-related activities under § 165.77 would be affected. Rather, the smaller or larger surcharge, like the decrease or increase in Radaj's exposure to other criminal penalties, relates only to his number of convictions.
¶ 31. As is clear from the statutes, the DNA surcharge is used to cover the cost of the DNA "analysis" of the biological specimen that the circuit court must order a defendant to provide at the time the court orders the surcharge. See Wis. Stat. §§ 973.046(lr) and 973.047(H). Although there is no burden on the State, we note that the State does not suggest, and could not seriously suggest, that the court must order (and that the state crime laboratories must analyze) as many biological specimens as there are convictions. See § 973.047(H) (stating that the court shall require the defendant to submit "a" biological specimen). Thus, we fail to see any link between the initial DNA analysis and the number of convictions.
¶ 32. Other costs that may come later under Wis. Stat. § 165.77 include the cost of comparing the defendant's DNA profile to the DNA profile of other biological specimens collected as part of a future investigation. See Wis. Stat. § 165.77(2)(a)l.a. and 2. and (3). However, we can conceive of no reason why such costs would generally increase in proportion to the number of convictions, let alone in direct proportion to the number of convictions.
¶ 33. As we understand it, the State's only argument for why the per-conviction surcharge is rational and not excessive in relation to its intended purpose is *650that the surcharge is generally small in amount as compared to the maximum fine a defendant may receive. The State notes, for example, that the $1,000 surcharge imposed on Radaj is only 1% of the maximum fine for Radaj's four crimes. The State points to In re DNA in which the Fourth Circuit Court of Appeals said that the "relatively small size of the fee" suggested that the fee was not punitive. See In re DNA, 561 F.3d at 300. However, this statement was made in the context of discussing the size of the fee in relation to its designated purpose of offsetting DNA expenses, not the size of the fee compared with criminal sanctions. A comparison with the maximum criminal fine a defendant might receive is not helpful.
¶ 34. We acknowledge that the burden is on Radaj to show by the "clearest proof' that there is no rational connection between the method of calculating the surcharge and the costs the surcharge is intended to fund. See Kester, 347 Wis. 2d 334, ¶ 22. We further acknowledge that Radaj did not attempt to present affirmative evidence, such as from a State official, verifying that costs under Wis. Stat. § 165.77 have little or no relation to the number of convictions at a given sentencing. However, we are satisfied that this is a matter that can be resolved by applying the statutory language and common sense. Nothing in the State's briefing suggests otherwise.
¶ 35. Accordingly, we conclude that the $1,000 DNA surcharge assessed against Radaj (four felonies x $250) as required under the new DNA surcharge statute is not rationally connected and is excessive in relation to the surcharge's intended purpose, and that its effect is to serve traditionally punitive aims. Based on that conclusion, we further conclude that, on bal*651anee, the surcharge has a punitive effect and, therefore, the statute is an unconstitutional ex post facto law as applied to Radaj.
¶ 36. In sum, the provision of the new DNA surcharge statute that we find to be dispositive, when applied to defendants receiving a sentence on multiple convictions, is the requirement that the surcharge increase with each conviction. We do not opine on other topics that the parties have chosen to ignore or largely ignore. Specifically, as we have indicated, we do not weigh in on whether the result might be different if Radaj had been convicted of a single felony carrying with it a mandatory $250 surcharge, rather than the prior discretionary $250 surcharge. We also do not opine on Radaj's passing reference in his reply brief to the idea that the difference between the $200 amount for misdemeanor convictions and the $250 amount for felony convictions suggests that the surcharge is punitive. See n.6, supra.
D. Remedy
¶ 37. Having concluded that the new DNA surcharge statute, Wis. Stat. § 973.046, is an unconstitutional ex post facto law as applied to Radaj and his multiple felony convictions, the question remains what remedy Radaj should receive. Only Radaj addresses remedy. He argues that the proper remedy is for us to remand with directions that the circuit court apply the surcharge statute that was in effect when Radaj committed his crimes.
f 38. The State fails to respond to Radaj's remedy argument, even though it is not apparent that the remedy Radaj requests is the only or best option. Thus, *652we conclude that the best course is to adopt Radaj's suggestion that we treat the State's failure to respond to Radaj's remedy argument as a concession. Accordingly, without deciding whether a different remedy could be appropriate, we rely on the State's concession to remand with directions that the circuit court apply the surcharge statute that was in effect when Radaj committed his crimes. Under that statute, the circuit court exercises discretion to determine whether Radaj should be assessed a $250 DNA surcharge. See Wis. Stat. § 973.046(1g) (2011-12); State v. Cherry, 2008 WI App 80, ¶ 5, 312 Wis. 2d 203, 752 N.W.2d 393.
Conclusion
¶ 39. For the reasons stated above, we reverse the part of the circuit court's judgment imposing the DNA surcharge. We also reverse the order denying Radaj's request for postconviction relief. We remand for the circuit court to apply the DNA surcharge statute that was in effect when Radaj committed his crimes.
By the Court. — Judgment affirmed in part, reversed in part; order reversed and cause remanded for further proceedings.
All references to the Wisconsin Statutes are to the 2013-14 version unless otherwise noted.
Article I, Section 9 of the United States Constitution states: "No bill of attainder or ex post facto law shall be passed." Article I, section 12 of the Wisconsin Constitution states: "No bill of attainder, ex post facto law, nor any law impairing the obligation of contracts, shall ever be passed ... ."
We follow the parties' lead, and assume that the prior statute authorized only a single $250 surcharge at a sentencing because the statute speaks in terms of "a [DNA] analysis surcharge of $250." See Wis. Stat. § 973.046(lg) and (lr) (2011 — 12) (emphasis added). Indeed, the State's ex post facto argument would make little sense if the prior law, like the new law, authorized a DNA surcharge that increased $250 for each felony conviction.
Wisconsin Stat. § 973.046(lr) provides:
If a court imposes a sentence or places a person on probation, the court shall impose a deoxyribonucleic acid analysis surcharge, calculated as follows:
(a) For each conviction for a felony, $250.
(b) For each conviction for a misdemeanor, $200.
One exception to this is that, because of differing effective dates under the new statutory scheme, there was a period of time under the new statutory scheme during which the court had to impose a DNA surcharge on misdemeanants even though the court did not need to require those misdemeanants to provide a DNA specimen. See 2013 Wis. Act 20, §§ 2355-2356, 9426. Whether there is an ex post facto problem as to those misdemeanants is the subject of a different appeal, State v. Elward, 2015 WI App 51, 363 Wis. 2d 628, 866 N.W.2d 756.
Another difference between the Wisconsin scheme and schemes from other states that the parties reference in passing is that now, under the revised DNA surcharge statute, the amount of the surcharge per conviction is greater for felonies than for misdemeanors. We have no reason to think this difference is tied to a difference in DNA-analysis-related costs for felony convictions and for misdemeanor convictions. Differentiating misdemeanors and felonies seemingly has implications for both the "intent" and "effect" parts of the ex post facto test, but we need not address those implications here because, regardless of such a possibility, we identify a different ex post facto problem with the DNA surcharge statute as applied to Radaj.