Pan-Pacific and Low Ball Cable Television Company appeals from the district *596 court’s order imposing sanctions in the amount of $161,720.36, pursuant to Fed. R.Civ.P. 11. The issue of sanctions was before the district court on remand, following our reversal of the imposition of sanctions on Farrow, Schildhause & Wilson, the law firm representing Low Ball. See Pan-Pacific and Low Ball Cable Television v. Pacific Union, 919 F.2d 145 (9th Cir.1990).

I.

In remanding for further proceedings consistent with Pavelic & LeFlore v. Marvel Entertainment Group, 493 U.S. 120 , 110 S.Ct. 456 , 107 L.Ed.2d 438 (1989), we noted that “upon remand, all the proper parties will be before the district court, should it wish to impose Rule 11 sanctions against someone other than the law firm.” Pan-Pacific, mem. disp. at 3. Low Ball now attacks the district court’s power to sanction it.

Low Ball argues that the district court’s initial decision to sanction the law firm divested that court of the power to sanction Low Ball on remand. Low Ball insists that the district court implicitly exonerated it by imposing sanctions only on the law firm, and that Pacific Union’s failure to appeal the implicit exoneration bars it now from seeking sanctions against Low Ball. We reject the argument.

The district court may not reconsider matters decided by us on the first appeal, but it may address any issue that we did not dispose of either expressly or impliedly. Nguyen v. United States, 792 F.2d 1500, 1502 (9th Cir.1986). Gf. Quern v. Jordan, 440 U.S. 332 , 347 n. 18, 99 S.Ct. 1139 , 1148 n. 18, 59 L.Ed.2d 358 (1979) (“While a mandate is controlling as to matters within its compass, on the remand a lower court is free as to other issues.”). Although we did not expressly rule on the propriety of imposing sanctions on Low Ball, our decision specifically contemplated the imposition of sanctions upon “all the proper parties,” which include the signer of the pleadings and the represented party. See Fed.R.Civ.P. 11.

In Willy v. Coastal Corp., — U.S.-, -, 112 S.Ct. 1076, 1080-81 , 117 L.Ed.2d 280 (1992), the Supreme Court upheld the imposition of sanctions against a represented party in a case in which it was later determined that the district court had lacked subject-matter jurisdiction over the litigation. The Court reasoned that the sanction order was “collateral to the merits,” and that “the interest in having rules of procedure obeyed ... does not disappear upon a subsequent determination that the court was without ... jurisdiction.” Id.

In Cooter & Gell v. Hartmarx Corp., 496 U.S. 384 , 110 S.Ct. 2447 , 110 L.Ed.2d 359 (1989), the Court upheld an award of sanctions against a represented party, even though the sanctions were imposed after the party had dismissed voluntarily the lawsuit that formed the basis for the sanctions. The Court reasoned that once the federal court's jurisdiction was invoked, the court could consider both the merits of the action and any motion for Rule 11 sanctions deriving therefrom. Id. at 395 , 110 S.Ct. at 2455. The Court specifically stated that sanctions may be imposed “after the principal suit has been terminated.” Id. at 396, 110 S.Ct. at 2456.

Low Ball’s argument that the district court lacked the power to sanction it fails. Just as the voluntary dismissal did not “expunge the Rule 11 violation” in Cooter, id. at 395, 110 S.Ct. at 2455, the Supreme Court’s intervening decision in Pavelic did not eliminate the violation here.

Pacific Union’s failure to file a cross-appeal does not bar it from seeking sanctions against the plaintiff. Once an initial appeal has been filed, “a cross-appeal is only the proper procedure, not a jurisdictional prerequisite.” Bryant v. Technical Research Co., 654 F.2d 1337, 1341 (9th Cir.1981) (internal quotation and citation omitted). Further, since Pacific Union received the relief it requested, no cross-appeal was necessary. See United States v. Raines, 362 U.S. 17 , 27 n. 7, 80 S.Ct. 519 , 526 n. 7, 4 L.Ed.2d 524 (1959).

*597 II.

The district court abused its discretion by sanctioning the law firm. The court did not abuse its discretion by sanctioning Low Ball for the frivolous state claims brought by it against Pacific Union.

Low Ball acted throughout this litigation through Harold Farrow, its general partner and senior partner at the law firm. The record demonstrates that Low Ball, through Farrow, was the “catalyst” behind the underlying action. See ChevronChevron, U.S.A, Inc. v. Hand, 763 F.2d 1184, 1187 (10th Cir.1985). The record also shows that Low Ball was well-positioned to investigate the facts supporting its claims. See Business Guides v. Chromatic Communications Enter., 498 U.S. 533 , —, 111 S.Ct. 922, 932 , 112 L.Ed.2d 1140 (1991) (“Quite often it is the client, not the attorney, who is better positioned to investigate the facts supporting a paper or pleading.”). Nevertheless, Low Ball failed to make a reasonable inquiry into the bases of its state law claims.

The tortious interference with contract claim was not previously based on a conspiracy theory. The district court properly found that claim frivolous.

The district court also properly determined that Low Ball’s allegations of unfair competition were based on an insufficient inquiry into the factual and legal bases for its claim. Low Ball has failed to identify adequately the basis for its claim of false advertising or for its allegations of “kickbacks.” The other state law claims were equally frivolous.

Low Ball argues that it was denied due process when the district court refused on remand to hear further arguments concerning the frivolousness of its claims. Low Ball is entitled to: (1) notice that the court is considering sanctions against it, and (2) an opportunity to be heard in opposition, see Hudson v. Moore Business Forms, 898 F.2d 684 , 686 (9th Cir.1990), but no more. Prior to imposing sanctions on the law firm, the court conducted a full-scale hearing, at which both the firm and Low Ball were given ample opportunity to plead their respective cases in opposition to sanctions. Due process does not entitle Low Ball to a second hearing on this issue.

III.

Low Ball argues that its non-frivolous federal claims create a “safe harbor” for its frivolous state law claims. We reject the argument. See Townsend v. Holman Consulting Corp., 929 F.2d 1358, 1363 (9th Cir.1990).

IY.

The district court erred by including in the sanction award Pacific Union’s expenses, including attorney’s fees, incurred in prosecuting the Rule 11 motion and in opposing Low Ball’s motion to reconsider the Rule 11 award. See Lockary v. Kayfetz, 974 F.2d 1166, 1178 (9th Cir.1992). These costs were not incurred “because of” Low Ball’s frivolous claims. See id. Nor was the motion to reconsider itself sanc-tionable. Pacific Union concedes, as it must, that the award should be reformulated accordingly.

The original award was for $161,720.36. This amount should be reduced by: (1) $26,-824.73 incurred by Pacific Union in bringing the Rule 11 motion; (2) $28,222.05 incurred by Pacific Union in litigating the amount of the Rule 11 award; and (3) $5,068.45 incurred by Pacific Union in opposing Low Ball’s motion to reconsider. Pacific Union is therefore entitled to $101,-605.13 plus accumulated interest. The parties shall bear their own costs on appeal.

AFFIRMED IN PART, REVERSED IN PART.