We address here the one remaining issue in this complex securities fraud suit arising out of an ill-fated oil-drilling project. The plaintiffs’ claim, in a nutshell, is that the defendants fraudulently lured them into investing in a project to drill oil wells on land *909in which the defendants fully knew there wasn’t any oil to be found.1 Terrence Dono-hoe and 58 other aggrieved investors brought suit against Consolidated Operating & Production Corporation (COPCO) and its principals and shareholders: Jack Nortman, Mor-ando Berrettini, Dennis Bridges and two companies that Bridges owned and operated (Ona Drilling Corporation and Onshore Rig Corporation). Bridges, it now appears, defrauded everyone. But he entered bankruptcy and the default judgments against his two companies (that never responded to the complaint) are likely of little value. That left Nortman, Berrettini and COPCO as the remaining defendants.
The amended complaint offered various theories of liability, primarily violation of the anti-fraud and registration requirements of the federal securities laws, together with RICO and state law theories. Finding that there was no evidence of either recklessness or intent to defraud (bad faith), the district court granted summary judgment in favor of the defendants on most of the claims. 736 F.Supp. 845. The only claim that did not contain a scienter requirement was the contention that the defendants sold a security by means of a misleading communication, in violation of § 12(2) of the 1933 Act, 15 U.S.C. § 771(2). But, when that count was dismissed on statute of limitations grounds, 763 F.Supp. 315, the entire action was dismissed with prejudice.
The plaintiffs appealed. While we otherwise affirmed the district court’s entry of summary judgment, we observed that the court, in a lengthy and otherwise carefully detailed opinion, failed to address the argument that Nortman and Berrettini may have “controlled” Bridges, and thus be liable for Ms malfeasance under a “control person” theory. We therefore remanded the matter to the district court for its consideration of this question. 982 F.2d at 1137.
On remand, the district court suggested that we had been led astray by the plaintiffs’ misleading arguments on appeal. The court had not addressed the control person theory the first time, the court said, because no such allegation had been made in the complaint. While in their complaint the plaintiffs alleged that Nortman and Berrettini controlled COP-CO, the plaintiffs never claimed Nortman and Berrettini controlled Bridges. Complaint ¶ 5.7. The district court therefore concluded that our decision to remand the case for its further consideration was, with characteristic understatement, “clearly erroneous.” But this conclusion, in light of the hierarchal structure of the federal judiciary, left the district court a bit uneasy. It therefore went on to suggest, with a distinct note of skepticism, that perhaps we wanted to allow the plaintiffs to make this argument despite their failure to make such an allegation in their complaint. It therefore also examined the merits of this contention.
To that end, it noted that a defendant’s good faith is an affirmative defense to a claim of control person liability. Here, the court asserted, essentially the same evidence of the defendants’ good faith that led it to grant summary judgment on the fraud claims also suggests that they made out an affirmative defense on the control person theory. It therefore granted summary judgment on the control person liability theory, and again dismissed the action with prejudice. The plaintiffs again appeal.
I
First a few words on the district court’s suggestion (though perhaps in dicta) that our decision to remand this case for its consideration of the control person theory was clearly erroneous. On this point, there are two questions. First, whether a district court may ignore (though the district court here did not) a court of appeals’ mandate on the grounds that the higher court’s decision was “clearly erroneous,” and second whether our *910previous decision in this case in fact represented error, clear or otherwise.
A
The law of the case doctrine typically provides that “when a court decides upon a rule of law, that decision should continue to govern the same issues in subsequent stages in the same case.” Arizona v. California, 460 U.S. 605, 618, 103 S.Ct. 1382, 1391, 75 L.Ed.2d 318 (1983). The doctrine applies not only to the previous decisions of the same court, but also to prior determinations of a coordinate court. Christianson v. Colt Industries Operating Corp., 486 U.S. 800, 815-18, 108 S.Ct. 2166, 2177-79, 100 L.Ed.2d 811 (1988). And it of course requires a district court to follow an appeals court’s mandate on remand. “When matters are decided by an appellate court, its rulings, unless reversed by it or by a superior court, bind the lower court.” Insurance Group Comm. v. Denver & R.G. W. R.R., 329 U.S. 607, 612, 67 S.Ct. 583, 585, 91 L.Ed. 547 (1947). “Whatever was before the court, and is disposed of, is considered as finally settled. The inferior court is bound by the decree as the law of the case, and must carry it into execution, according to the mandate.” Sibbald v. United States, 37 U.S. (12 Pet.) 488, 492, 9 L.Ed. 1167 (1838).
The law of the case doctrine is, however, subject to a few exceptions. Most notably, it is “not improper for a court to depart from a prior holding if convinced that it is clearly erroneous and would work a manifest injustice.” Arizona v. California, 460 U.S. at 618 n. 5, 103 S.Ct. at 1391 n. 5. True enough, but does that invitation apply only to a court departing from its own prior holding, or may a lower court find a reviewing court’s decision to be clearly erroneous?
A lower court that thinks an appeals court’s ruling to be clearly erroneous is in a position not unlike that of a court forced to decide a case that appears to be controlled by a higher court precedent that it considers wrongly decided. What if the lower court expects the higher court, if given a chance, to see the error in its ways, and reverse the “erroneous” precedent? The Supreme Court has said that courts of appeals should not anticipate such reversals by declining to follow a ease on point. Rather, the “Court of Appeals should follow the case which directly controls, leaving to this Court the prerogative of overruling its own decisions.” Rodriguez de Quijas v. Shearson/American Express Inc., 490 U.S. 477, 484, 109 S.Ct. 1917, 1921-22, 104 L.Ed.2d 526 (1989).
Such a strict prohibition on what might be called “underruling” is perhaps less imperative with respect to district courts anticipating that we might overrule one of our precedents, given the availability, at this level, of review as a matter of right. But our cases nonetheless take a firm position on the matter. “Ours is a hierarchical judiciary, and judges of inferior courts must carry out decisions they believe mistaken. A district judge who thinks new evidence or better argument ‘refutes’ one of our decisions should report his conclusions while applying the existing law of the circuit.” Gacy v. Welborn, 994 F.2d 305, 310 (7th Cir.), cert. denied, — U.S. -, 114 S.Ct. 269, 126 L.Ed.2d 220 (1993).2 Compare Evan H. Caminker, Why Must Inferior Courts Obey Superior Court Precedents?, 46 Stan.L.Rev. 817, 867 (1994) (“The duty to obey circuit precedent generally is dictated by the balance of salient values; the extreme rigidity of the duty, while eminently sensible, reflects a far more controversial judgment.”) (emphasis in original).
The law of the case doctrine is analogous. A district court that disagrees with an appeals court’s decision to remand a case for its further consideration (and wants to invoke the clearly erroneous exception to the law of the case doctrine) is in a position similar to the lower court that disagrees with controlling precedent. It should follow our suggestion in Gacy: signal its disagreement, but carry out the mandate. Cf. Sibbald, 37 U.S. (12 Pet.) at 492 (“[On remand, the lower court] cannot vary [the mandate], or examine it for any other purpose than execution, or *911give any other or further relief, or review it upon any matter decided on appeal for error apparent, or intermeddle with it, further than to settle so much as has been remanded.”); Houck v. Folding Carton Administration Committee, 881 F.2d 494, 499 (7th Cir.1989), cert. denied, 494 U.S. 1026, 110 S.Ct. 1471, 108 L.Ed.2d 609 (1990) (court of appeals’ “directives cannot, in ordinary circumstances, be avoided or ignored by either the district court or by the parties”).
It thus appears that the district court treated this case in exactly the appropriate manner. The court “found” that the matter was remanded for its further consideration only because the plaintiffs succeeded in “misleading our Court of Appeals into a ‘clearly erroneous’ ruling,” 833 F.Supp. at 727, but noted that for “both policy and jurisprudential reasons this Court would not be prepared to rest on such a determination short of the merits, even if it were empowered to do so.” Id.3 It therefore followed the mandate, considering—as instructed—the claim that the defendants might be liable for Bridges’ fraud on a control person theory. Such a procedure, it seems to us, best accommodates the various judicial interests in assuring both the correctness of our decisions (by leading us to re-examine them when a district court has qualms) while at the same time guaranteeing the stability and predictability that are the purpose of our hierarchical judicial structure.
B
On the merits, though, it is not at all clear to us that the plaintiffs failed sufficiently to allege that Nortman and Berrettini controlled Bridges and are therefore liable for his fraud. It is true that the complaint does not spell out such a theory with perfect clarity. Rather than expressly alleging that Nortman and Berrettini controlled Bridges, it alleges only that they controlled COPCO. But Bridges (along with Nortman and Ber-rettini) was a COPCO partner. There is surely a discernable difference between saying that two partners “controlled” the third partner and claiming that the two controlled the partnership. But it is not entirely obvious to us—in light of the liberal federal pleading rules and the Supreme Court’s admonition that a complaint need only give the defendant “fair notice of what the plaintiffs claim is and the grounds upon which it rests,” Conley v. Gibson, 365 U.S. 41, 48, 78 S.Ct. 99, 103, 2 L.Ed.2d 80 (1957)—that the complaint here was inadequate. We can in any event assume, for the purposes of the section that follows, that the complaint did sufficiently put Nortman and Berrettini on notice of the claim that they controlled Bridges for this theory of liability to survive.
II
Given our assumption that such a claim is adequately alleged, the question is whether the defendants are entitled to summary judgment on the claim that they “controlled” Bridges and are thus liable for his fraud. Section 20(a) of the 1934 Act, 15 U.S.C. § 78t(a), and Section 15 of the 1933 Act, 15 U.S.C. § 77o, both set out “control person” liability—providing a vehicle to hold one defendant vicariously liable for the securities violations committed by another.4
As we recognized in considering the first appeal in this case, our opinion in Harrison v. Dean Witter Reynolds Inc., 974 F.2d 873, 880-81 (7th Cir.1992), cert. denied, — U.S. -, 113 S.Ct. 2994, 125 L.Ed.2d 688 (1993), sets out a two-prong test for determining control person liability. 982 F.2d at 1138. First, the “control person” needs to have actually exercised general control over the operations of the wrongdoer, and second, the control person must have had the power *912or ability — even if not exercised — to control the specific transaction or activity that is alleged to give rise to liability. It was in this case clear enough that because Bridges used COPCO as a vehicle to perpetrate fraud, and because Nortman and Berrettini between them had majority control and played an active role in the day to day operations of the business, that they could be seen as “controlling” Bridges. 982 F.2d at 1138-39.
We further recognized, however, that good faith is a defense to control person liability. See Harrison, 974 F.2d at 881-82; Fey v. Walston & Co., Inc., 493 F.2d 1036, 1051 (7th Cir.1974); Hollinger v. Titan Capital Corp., 914 F.2d 1564, 1574-75 (9th Cir.1990) (en bane), cert. denied, 499 U.S. 976, 111 S.Ct. 1621, 113 L.Ed.2d 719 (1991). But unlike the plaintiffs’ other claims in which the defendant’s bad faith was an element of the offense, because good faith was an affirmative defense to control person liability, the burden of proving good faith was on the defendants. Hence, while we had otherwise concluded that the plaintiffs had not brought forward sufficient evidence of the defendants’ bad faith for their claims to go forward, we sent the ease back to the district court to decide whether the plaintiffs’ evidence of their own good faith entitled them to summary judgment on the “control person” theory.
Control person liability is most frequently encountered when a defendant seeks to hold a brokerage house liable for the securities violations committed by its employees. In that context, as the district court observed on remand, good faith is typically determined by examining whether the control person set up and enforced with reasonable diligence sufficient systems of internal supervision and control designed to detect securities violations.
But this type of analysis was obviously designed for, and cannot sensibly be applied outside of, the respondeat superior context. Thus, in other contexts the Fifth Circuit has employed a more flexible approach, asking simply whether the control person has taken reasonable measures, in light of the situation, to prevent the securities violation. “The test of whether the controlling person has done enough to prevent the violation depends on what he could have done under the circumstances.” G.A. Thompson & Co. v. Partridge, 636 F.2d 945, 959 (5th Cir.1981).
The Supreme Court has also suggested, though this is not a factor that — -until recently — our cases have emphasized much, that the good faith defense exculpates defendants whose behavior is merely negligent. See Ernst & Ernst v. Hochfelder, 425 U.S. 185, 209 n. 28, 96 S.Ct. 1375, 1389 n. 28, 47 L.Ed.2d 668 (1976). “The controlling person must also act recklessly; negligence alone is insufficient.” Monieson v. Commodities Futures Trading Commission, 996 F.2d 852, 860 (7th Cir.1993). It therefore seems to us that our task is to examine what the defendants could have done under the circumstances to prevent the violation, and then ask whether the defendants — aware that they could take such measures — decided not to. This is just to say that we are to determine whether there is a genuine issue of fact regarding the defendants’ recklessness. We agree with the district court that the defendants have shown that there is not.
As the district court noted in originally concluding that the defendants lacked bad faith, 736 F.Supp. at 874-76, the defendants conducted an extensive check into Bridges’ background, set up an escrow system to cheek the disbursement of money into Ona’s bank account and regularly checked up on Bridges’ work. Even so, the defendants, who themselves controlled the administrative and financial aspects of COPCO’s business, were required to rely heavily on Bridges’ superior technical expertise. And there is no suggestion in the record that the defendants had any reason to believe that the sources to whom they looked in evaluating Bridges would prove unreliable. And perhaps most importantly, the defendants invested a large amount of their own energies and funds (more than $100,000) in this project, making it fairly clear that their actions taken with respect to the undertaking were in good faith, as that term is commonly understood.
We therefore agree with the district court that the defendants were entitled to summary judgment on the arguable claim that they “controlled” Bridges since their good *913faith represents an affirmative defense to control person liability. Hence, since we would in any event affirm the entry of summary judgment, we have no need to examine further whether this claim was — in fact— sufficiently alleged in the complaint to justify our remand. The judgment of the district court is accordingly
AFFIRMED.
. The five published opinions in this action have now filled 106 pages of the Federal Reporter and Federal Supplement. See 982 F.2d 1130 (7th Cir.1992); 833 F.Supp. 719 (N.D.Ill.1993); 763 F.Supp. 315 (N.D.Ill.1991); 736 F.Supp. 845 (N.D.Ill.1990); 691 F.Supp. 109 (N.D.Ill.1988). We add as little as necessary to that flurry of paper, assuming the reader’s familiarity with these previous opinions and relating the facts only as they are imperative to the disposition of the remaining issue in this litigation.
. While Gacy’s suggestion is surely on target in a traditional context, where a district court believes that one of our precedents is refuted by "better argument,1' its application to Gacy itself—a challenge to precedent presented by “new evidence”—is somewhat more problematic.
. It is our conclusion here that the district court was not so empowered.
. Section 20(a) of the 1934 Act provides that "[ejveiy person who, directly or indirectly, controls any person liable under any provision of this chapter or any rule or regulation thereunder shall also be liable jointly and severally with and to the same extent as such controlled person.” Section 15 of the 1933 Act is parallel, though control person liability is there limited to actions under sections 11 and 12 of that Act. See generally 2 Thomas Lee Hazen, The Law of Securities Regulation, § 13.15 (2d ed. 1990); Comment, Vicarious Liability of Controlling Persons: Re-spondeat Superior and the Securities Acts—A Reversible Consensus in the Circuits, 42 Emory L J. 313 (1993).