Chad Conrad filed a class action against Boiron for deceptive marketing, but he was left with only his individual claim after the district court refused to certify his proposed class. About a year later Boiron offered Conrad $5,025, more than he could hope to win at trial. Conrad does not want to accept the money because it will moot his claim; Boiron wants to force him to take it for the same reason. The district court refused to certify Conrad’s proposed class and found his individual claim moot. We conclude, in keeping with our decision in Fulton Dental, LLC v. Bisco, Inc., 860 F.3d 541 (7th Cir. 2017), that the latter decision was in error, because an -unaccepted offer cannot moot a case. There are other measures available to address the problem (if it exists here) of “unreasonably and vexatiously” persisting in litigation, see, e.g., 28 U.S.C. § 1927, but the district court has yet to decide whether they should be used. We therefore remand this case to the district court for further proceedings.
I
Boiron makes homeopathic products, including an over-the-counter remedy called Oscillococcinum (“Oscillo”) that retails for between $12 and $20, depending on whether one buys a six, twelve, or thirty-dose package. Bohn v. Boiron, Inc., 2013 WL 3975126, at *1 (N.D. Ill. Aug. 1, 2013). Oscillo is made by mixing one percent Anas Barbariae Hepatis et Cordis Extrac-tum — that is, duck hearts and livers — with 99 percent water, repeating the dilution process 200 times, and then selling the result in pill form. The repeated dilutions render the finished product nothing more than a placebo. Boiron’s claim that Oscillo has a therapeutic effect on flu symptoms is thus highly doubtful. Aggrieved customers caught on at some point, and in 2011 they filed a class action against the company in the Southern District of California over its deceptive marketing. In October 2012, Boi-ron and the class agreed to a broad settlement that covered over 200 of the company’s products (including Oscillo) purchased between January 1, 2000 and July 27, 2012. Gallucci v. Boiron, Inc., 2012 WL 5359485 (S.D. Cal. Oct. 31, 2012), aff'd sub nom. Gallucci v. Gonzales, 603 Fed.Appx. 533 (9th Cir. 2015). In relevant part, the settlement required Boiron to (1) pay refunds to past buyers, (2) revise its labels to make them accurate, and (3) let future unhappy customers request refunds within 14 days of purchase (the company calls this the “Boiron Promise”). Boiron went one step further; it now informs customers that they have 30 days from purchase to request a refund. See Boiron Promise, BOI-RON, http://www.boironusa.com/promise/ (last visited Aug. 22, 2017) (“Boiron Promise Webpage”).
Some of the class members were not satisfied with this outcome, and so they opted out of the Gallucci settlement. Attorneys representing the opt-outs filed new class actions, raising essentially the same claims against Boiron, in California and Illinois. When the district courts found the class representatives inadequate, counsel tried to swap in replacements. In the Illinois case, the prospective representative was the current plaintiff, Chad Conrad. (Boiron eventually prevailed in the California case, and so it does not concern us further.) Yet before the Illinois substitution could occur, the then-lead plaintiff accepted Boiron’s offer of judgment, prompting the district court to terminate *539the case. Boiron also offered Conrad $25 (more than he had paid for the Oscillo) plus attorney’s fees and costs to settle his claim, but he rejected the offer and filed the complaint that kicked off the current suit on November 4, 2013. Eight months of preliminary proceedings followed, at which point the district court stayed the case pending the Ninth Circuit’s resolution of the appeal of the October 2012 settlement. That court ultimately upheld the settlement, and the district court lifted its stay on August 13, 2015.
Two weeks later, Boiron filed a motion to dismiss, which for the most part the district court granted. The court found that Conrad was an inadequate class representative because his suit would provide little benefit beyond Boiron’s existing refund guarantee; it also found that Conrad lacked standing to pursue injunctive relief (a ban on marketing Oscillo as a flu remedy) under the Illinois Consumer Fraud Act since Conrad himself would not be duped by Boiron’s misleading claims again. We denied Conrad’s request to appeal the denial of class certification in February 2016, leaving him with only his individual damages claim. After still more proceedings, the district judge granted Boiron’s motion under Federal Rule of Civil Procedure 67 to deposit $5,025 with the court — above the maximum Conrad could recover — -in order to moot his claim. Boiron deposited the funds, and the district court dismissed the case as moot on September 20, 2016. This appeal followed.
II
Conrad’s main arguments are straightforward: he attacks both the court’s refusal to certify the class and its rejection of his individual claim based on Boiron’s use of Rule 67 to try to moot the case. We review the denial of class certification for abuse of discretion, and we consider the mootness ruling de novo. Messner v. Northshore Univ. HealthSystem, 669 F.3d 802, 811 (7th Cir. 2012); Stevens v. Hous. Auth. of S. Bend, Ind., 663 F.3d 300, 306 (7th Cir. 2011).
A
We begin with Conrad’s effort to represent what remains of the class of Oscillo purchasers after the Gallucci settlement. Federal Rule of Civil Procedure 23(a) conditions class certification on “four requirements — numerosity, commonality, typicality, and adequate representation.” Wal-Mart Stores, Inc. v. Dukes, 564 U.S. 338, 349, 131 S.Ct. 2541, 180 L.Ed.2d 374 (2011). This case turns on adequacy, for an aspiring lead plaintiff such as Conrad is entitled to represent a class only if he “will fairly and adequately protect the interests of the class.” FED. R. CIV. P. 23(a)(4). In order to be an adequate representative, the named plaintiff must “be part of the class and possess the same interest and suffer the same injury as the class members.” Amchem Prod., Inc. v. Windsor, 521 U.S. 591, 625-26, 117 S.Ct. 2231, 138 L.Ed.2d 689 (1997) (internal quotation marks and citation omitted). In addition, the court must be satisfied that the plaintiff will keep the interests of the entire class at the forefront. Conrad’s case brings to mind our comment in In re Aqua Dots Products Liability Litigation, 654 F.3d 748, 752 (7th Cir. 2011) (“Aqua Dots”), that “[a] representative who proposes that high transaction costs (notice and attorneys’ fees) be incurred at the class members’ expense to obtain a refund that already is on offer is not adequately protecting the class members’ interests.”
In Aqua Dots, the manufacturer- of the eponymous toys re-called them because they were potentially toxic. The recall notice told buyers that they could exchange the Aqua Dots for a non-defective replace*540ment or a different, comparably priced toy. Notably, it did not mention any refunds, though they were provided upon request. A group of buyers challenged the recall program through a class action, alleging that the relief the company offered was inadequate. The district court refused to certify the class, and we affirmed because the putative class representative failed to satisfy Rule 23(a)(4)’s adequacy requirement.
Aqua Dots demonstrates that there is more to adequacy than simple membership in a group. As we said in Eubank v. Pella Corp., 753 F.3d 718, 719 (7th Cir. 2014), the “named [class] plaintiffs are the representatives of the class — fiduciaries of its members.... ” It is thus both -necessary and proper for the district court to consider whether the potential named representative will act in the best interests of the unnamed membei’s of the class. That was precisely our point in Aqua Dots. There, the product in question cost from $17 to $30. In re Aqua Dots Prod. Liab. Litig., 270 F.R.D. 377, 379 (N.D. Ill. 2010). Given the low price point, we were concerned that transaction costs might swallow all of any potential recovery. The same point applies here. Oscillo retails for between $12 and $20. Most .Oscillo buyers are protected not only by the Gallucci settlement, but also by the refund process Boiron now offers on its website (which is not limited to those who participated in the settlement).
There is another' important' similarity between our case and Aqua Dots — both proposed classes are relatively small. The class Conrad envisions is limited to relatively recent purchasers who have not taken advantage of the Boiron Promise, The combination of low-value claims and small class size is likely to make this another case in which “high transaction costs (notice and attorneys’ fees)” will leave class members with a negligible award. Aqua Dots, 654 F.3d at 752. Indeed, it is hard to see how the proposed class action benefits anyone but the attorneys who filed it, especially since this suit (to say nothing of its failed predecessor) has been rumbling on for years. Class actions driven by attorneys’ fees are notoriously troublesome.
Conrad responds that the Aqua Dots l’ecall was more generous than the “Boiron Promise,” and so there is more potential in the class-wide treatment he proposes. We agree with him that the Boiron Promise is poorly publicized and hard to use when compared to the Aqua Dots recall. Boiron does not mention the refund on Oscillo’s packaging nor does it display information about the refund prominently on its website. To the contrary, finding any information at all takes some digging. See Boiron Promise Webpage. And, astonishingly, Boi-ron requires that refunds be sent by “snail mail” rather than digitally. Color us unimpressed with this transparent attempt to put off dissatisfied customers. Boiron is happy to take Oscillo buyers’ money online, and so we see no reason why it cannot handle refunds the same way. See Oscillo, BOIRON, https://shop.boironusa.com/ medicine/oscillococcinum/.(last visited Aug. 22, 2017) (allowing online purchase of Os-cillo). More broadly, as digital commerce becomes ever-more embedded into American society, Boiron’s pretense that recalls and refunds (but not purchases) require resort to physical mail is hard to take seriously.
Nonetheless, taken as a whole, the Boi-ron Promise is comparable to the process we accepted in Aqua Dots. Boiron’s refund publicity, lackluster though it is, looks better when we consider that the Aqua Dots recall did. not even mention a refund. There, customers had to decide on their own to ask for one. The contrast between the two default positions is important — the *541typical Boiron Promise user receives a refund; the typical Aqua Dots buyer got a replacement product or a comparable toy. Compare Aqua Dots, 654 F.3d at 750 with Boiron Promise Webpage. All of this is to say that the remedies already in place for disappointed Boiron customers undermine. Conrad’s ability to show that he can bring any significant extra value to the absentee class members.
Conrad argues that, as a factual matter, discovery would reveal that the Boiron Promise is empty, and that aggrieved purchasers are not obtaining any relief. But there was enough information in the record to permit the district court to spot the similarities with Aqua Dots and to conclude that this case is not suitable for class treatment. It is hard to see how more discovery would change things. In one incarnation or another, this case has dragged on since 2013; it is a de facto continuation of the preceding 2011 suit, which was itself an outgrowth of the underlying California class action. The evidence is out there for all to see, and Conrad has given us no reason to think that there are any smoking guns left to uncover. His own actions reinforce this conclusion: he took no steps to pursue discovery between his 2013 motion for class certification and his last-ditch effort to avoid dismissal in 2016. We conclude, therefore, that the district court was well within .-its rights to refuse to certify Conrad’s proposed class. In so ruling, we stress that we place no significance on Boiron’s later effort to render Conrad’s individual case moot by buying him off with a Rule 67 deposit into the court’s registry. The denial of class certification stands on its own.
B
That leaves-. Conrad’s individual case, which does turn on the effect of Boiron’s payment of $5,026 into the court’s registry, pursuant to Federal Rule of Civil Procedure 67. In Fulton Dental, we addressed the question whether a defendant’s act of depositing with the court an amount that (if accepted) would fully satisfy a plaintiffs claim, rendered the plaintiffs .case moot. After a review of the Supreme Court’s decision in Campbell-Ewald Co. v. Gomez, _ U.S. _, 136 S.Ct. 663, 193 L.Ed.2d 571 (2016), as well as a careful look at the mechanics of Rule 67, we concluded that the answer was no. 860 F.3d at 545-46. See also Chapman v. First Index, Inc., 796 F.3d 783, 786-87 (7th Cir. 2015). Our reasoning in Fulton Dental, following that of the Supreme Court in Campbell-Ewald, was based on the law of contract. As the Court put it, “an unaccepted settlement offer or offer of judgment does not moot a plaintiffs case.” 136 S.Ct. at 672. We explained in Fulton Dental why a Rulé 67 offer for this purpose is equivalent to the Rule 68 offer that was involved in Campbell-Ewald. The court cannot accept an instrument made payable to a third party into its registry; checks are normally drawn to the clerk of the court and release is by order of the court. This fact prompted our statement in Fulton Dental that the process of depositing funds with the court and later withdrawing them in favor of a party is not a mechanical one. 860 F.3d at 545.
Boiron would like us to hold that at some point, a plaintiffs stubborn refusal to accept a generous settlement offer should be taken as the legal equivalent of acceptance; But we are aware of no such doctrine, and we are loathe to adopt such an ill-defined rule. The Supreme Court has never endorsed anything like this. To the contrary, it has recognized “the deep-rooted historic tradition that everyone should have his own. day in court.”. Taylor v. Sturgell, 553 U.S. 880, 892-93, 128 S.Ct. 2161, 171 L.Ed.2d 155 (2008) (internal quo*542tation marks omitted). That does not mean that every person will use that day in court in a way that is economically rational, and some will invoke the aid of the courts for impermissible purposes. But so-called negative-value cases are sometimes rational, if the party hopes to establish an important principle through the case. That said, there is no guarantee that litigation will not be abused. Cf. Prof'l Real Estate Investors, Inc. v. Columbia Pictures Indus., Inc., 508 U.S. 49, 113 S.Ct. 1920, 123 L.Ed.2d 611 (1993) (setting out the contours of the “sham” litigation doctrine for antitrust purposes).
The law has developed doctrines, such as the common-law tort of wrongful civil proceedings (related to the malicious prosecution tort that arises from criminal proceedings), to address abusive litigation. And free-standing claims are not the only option. Federal courts have an array of tools to address these problems. Prominent among them is 28 U.S.C. § 1927, which authorizes the court to sanction against “[a]ny attorney ... who so multiplies the proceedings in any case unreasonably and vexatiously ... .” Rule 11 of the Federal Rules of Civil Procedure also serves as a constraint on a lawyer’s ability to file a case that is not appropriately founded. If a case is based on diversity of citizenship, whether under the conventional rules of 28 U.S.C. § 1332(a) or (as here) the Class Action Fairness Act, 28 U.S.C. § 1332(d), if the plaintiff prevails but is awarded less than $75,000, “the district court may deny costs to the plaintiff and, in addition, may impose costs on the plaintiff.” 28 U.S.C. § 1332(b). If the defendant, rather than using the Rule 67 process that Boiron tried, uses the rule best suited for pre-trial offers of settlement — Rule 68 — and that offer is not accepted, then “[i]f the judgment that the offeree finally obtains is not more favorable than the unaccepted offer, the offeree must pay the costs incurred after the offer was made.” FED. R. CIV. P. 68(d). Finally, the courts have inherent power to punish abuses of process. Chambers v. NASCO, Inc., 501 U.S. 32, 111 S.Ct. 2123, 115 L.Ed.2d 27 (1991). We are not saying, at this juncture, that any of these measures is appropriate for Conrad’s case. The point is only that tools exist for the person who abuses the litigation process, but the tools do not include deemed acceptance of a proposed offer of settlement.
Before concluding, we should say a word about the district court’s conclusion that Conrad does not have standing to request injunctive relief under the Illinois Consumer Fraud Act (ICFA). See Summers v. Earth Island Inst., 555 U.S. 488, 493, 129 S.Ct. 1142, 173 L.Ed.2d 1 (2009) (plaintiff “bears the burden of showing that he has standing for each type of relief sought”). The court reasoned that Conrad, as an individual, knows about Boiron’s refund program and that he is fully aware of the fact that Oscillo is nothing but sugar water. No injunction could therefore redress any potential injury for him, and that lack of redressability defeats standing. See Spokeo, Inc. v. Robins, _ U.S. _, 136 S.Ct. 1540, 1547, 194 L.Ed.2d 635 (2016). We agree with that ruling. This is not a case like Laurens v. Volvo Cars of N. Am., LLC, No. 16-3829, 868 F.3d 622, 2017 WL 3598070 (7th Cir. Aug. 22, 2017), where class treatment was still a possibility and the record did not unequivocally foreclose the possibility of injunctive relief for the putative named plaintiff. In the present case, there will be no class, given our affirmance of the district court’s decision denying certification. If Conrad has a claim at all, it is an individual one for money only.
*543III
The district court did not abuse its discretion in denying class certification, and it correctly rejected Conrad’s individual claim for injunctive relief. It erred, however, insofar as it concluded that the passage of time meant that Conrad no longer had the legal right to reject Boiron’s offer of settlement. We therefore Affirm in part and Remand for further proceedings consistent with this opinion. Each party will bear its own costs on appeal.