ORDER

Marion Beaven, who is currently incarcerated at the Miami Correctional Facility in Indiana, appeals the district court’s dismissal of his civil rights suit seeking damages for his continued confinement. Because his suit is squarely precluded under Heck v. Humphrey, 512 U.S. 477, 114 S.Ct. 2364, 129 L.Ed.2d 383 (1994), we affirm.

I

BACKGROUND

In October 1994, Mr. Beaven was convicted of five counts of conspiracy to commit forgery and determined to be a habitual offender by an Indiana jury. Indiana judge Stephanie Roth sentenced him to twenty years’ imprisonment — five concurrent eight-year terms for the conspiracy convictions and a twelve-year consecutive sentence for the habitual offender determination. At sentencing, Judge Roth determined that he should be credited 97 days for the time he served in jail awaiting his trial and sentencing.1 Mr. Beaven, however, maintains that he spent 430 days in pretrial detention. By Mr. Beaven’s calculations, if those 430 days are credited towards his sentence and doubled pursuant to Indiana’s day-for-day good-time stat*637utes, see IncLCode § 35-50-6-3(a) and 4(a), he is entitled to immediate release. Mr. Beaven has unsuccessfully challenged the computation of his sentence through administrative channels, state post-conviction proceedings, and a petition for a writ of habeas corpus under 28 U.S.C. § 2254.

In December 2002, Mr. Beaven filed this suit under 42 U.S.C. § 1983 claiming that Judge Roth prevented him from receiving the presentence credit he is due in violation of his constitutional rights. He also named as defendants Stephan Scrogham, an Indianapolis police detective; William Young, the attorney who represented him at trial and sentencing; and Evelyn Turner, the Commissioner of the Indiana Department of Corrections. He alleges that Scrogham filed a false affidavit of probable cause charging that he was a habitual offender, Young “pretended” to be his appointed public defender and thereby obstructed his right to effective assistance of counsel during his trial and sentencing, and Turner miscalculated his good-time credits based on Judge Roth’s “defective abstract of judgment” and confined him longer than allowed by Indiana law. (Compl. at 2-3). He seeks one million dollars in damages from each defendant for each day of his continued incarceration.

The district court screened Mr. Beaven’s complaint pursuant to 28 U.S.C. § 1915A, and on January 7, 2003, dismissed the action for failure to state a claim on the basis of Heck, which holds that a state prisoner may not pursue a § 1983 claim seeking only damages that would, if successful, “necessarily imply the invalidity of his conviction or sentence” unless that conviction or sentence has been invalidated by a state tribunal or a federal court’s issuance of a writ of habeas corpus. 512 U.S. at 486-87, 114 S.Ct. 2364. The district court reasoned that Mr. Beaven’s claims of “having been improperly sentenced, having been impeded in a defense, or having had his judicial commitment improperly calculated ... could not be resolved in his favor without impugning his conviction or sentence.” (Appellant’s App. at 12.) Because he had failed to establish by a habeas corpus proceeding or its equivalent that his conviction or sentence was unlawful, the court concluded that, under Heck, his § 1983 suit could not proceed.

Shortly thereafter, Beaven filed a motion to vacate the dismissal (which the district court properly construed as a motion under Federal Rule of Civil Procedure 59(e)) on the ground that he had inadvertently omitted from his complaint allegations that the defendants falsified documents as part of a conspiracy to deprive him of the full amount of presentence credit. At the same time, he moved for leave to amend his complaint to add those allegations. The district court denied both motions, and this appeal followed.

II

ANALYSIS

On appeal, Mr. Beaven argues that Heck does not bar his § 1983 suit because he is merely challenging the procedures used to deny him presentence credit, not the resulting denial of that credit. His argument is frivolous. The argument is belied by his prayer for damages for each day that he has been “wrongfully imprisoned.” And, although the only remedy he seeks is damages, the gravamen of his claim is that, as a result of the defendants’ alleged misconduct, he was deprived of the presentence credit to which he was entitled. If the nature of the procedural challenge would necessarily imply the invalidity of the deprivation, then the claim is not cognizable under § 1983. See Edwards v. Balisok, 520 U.S. 641, 645, 117 S.Ct. 1584, 137 L.Ed.2d 906 (1997).

*638Here, the alleged procedural defects not only imply the invalidity of the department of correction’s refusal to grant Mr. Beaven presentence credit, but the state court’s judgment that he was entitled to only 97 days of credit. As a general rule, federal courts (other than the Supreme Court) have no subject matter jurisdiction to review state-court judgments, see Rooker v. Fid. Trust Co., 263 U.S. 413, 416, 44 S.Ct. 149, 68 L.Ed. 362 (1923); District of Columbia Ct. of App. v. Feldman, 460 U.S. 462, 482, 103 S.Ct. 1303, 75 L.Ed.2d 206 (1983), and litigants cannot avoid this rule by casting their complaints in the form of a federal civil rights action under § 1983, see Lewis v. Anderson, 308 F.3d 768, 772 (7th Cir. 2002); Maple Lanes, Inc. v. Mel Messer, 186 F.3d 823, 825 (7th Cir. 1999). Federal courts do have authority to review collaterally state-court judgments in criminal cases, but only through habeas corpus. See 28 U.S.C. §§ 2241, 2254; Preiser v. Rodriguez, 411 U.S. 475, 488-90, 93 S.Ct. 1827, 36 L.Ed.2d 439 (1973). Indeed, “habeas corpus is the exclusive remedy for a state prisoner who challenges the fact or duration of his confinement and seeks immediate or speedier release, even though such a claim may come within the literal terms of § 1983.” Heck, 512 U.S. at 481, 114 S.Ct. 2364 (citing Preiser, 411 U.S. at 488-90, 93 S.Ct. 1827). Accordingly, we have emphasized that “[sjtate prisoners who want to challenge their convictions, their sentences, or administrative orders revoking good-time credits or equivalent sentence-shortening devices, must seek habeas corpus, because they contest the fact or duration of custody.” Moran v. Sondalle, 218 F.3d 647, 650-51 (7th Cir. 2000) (per curiam).

The rationale of Heck is that prisoners should not be able to circumvent the established routes for challenging the lawfulness of their continued confinement through a suit for damages under § 1983. Miller v. Indiana Dep’t of Corr., 75 F.3d 330, 331 (7th Cir. 1996). Yet, that is precisely what Mr. Beaven has sought to do here. A state prisoner’s suit challenging the computation of his sentence is a suit challenging the duration of his confinement, and therefore, the appropriate vehicle to raise such a claim in federal court is a writ of habeas corpus under § 2254, after exhausting state remedies. See Moran, 218 F.3d at 650-51; Whitehead v. Johnson, 157 F.3d 384, 386 n. 1 (5th Cir. 1998) (per curiam). Having been unsuccessful at attacking the state court’s determination of his presentence credit through the proper channels, Mr. Beaven has disguised what is really a habeas corpus action as a suit for damages under § 1983.

Heck dictates that his suit cannot be maintained if the suit would, were it successful, imply that the determination was wrong. Mr. Beaven alleges that at sentencing the judge erred, his lawyer was ineffective, and the police detective falsified documents. He further alleges that the state department of corrections miscalculated his sentence based on the defective state-court judgment. As the district court concluded, resolving these claims in Mr. Beaven’s favor plainly would impugn the state-court’s judgment, and the lawfulness of his continued confinement. We have repeatedly held that such claims are precluded by Heck. See, e.g., Clemente v. Allen, 120 F.3d 703, 705 (7th Cir. 1997) (Bivens suit seeking damages for alleged miscalculation of federal prisoner’s sentence barred by Heck); Rooding v. Peters, 92 F.3d 578, 580-81 (7th Cir. 1996) (suit for damages under § 1983 for miscalculation of sentence credits did not accrue until plaintiff prevailed in state mandamus action); Miller, 75 F.3d at 331 (Heck precluded suit for damages under § 1983 for alleged denial of due process in determination of sentence credit classification). *639Likewise, because Mr. Beaven clearly “is challenging the lawfulness of his continued confinement, ... having failed to vindicate the challenge through the proper means he is barred from seeking vindication in this suit for damages.” Miller, 75 F.3d at 331.

Mr. Beaven also argues that the district court should have allowed him to amend his complaint to cure any deficiencies. But his request to amend was made after the court entered judgment dismissing the complaint, and courts need not grant post-judgment requests. Fed. R.Civ.P. 15(a); Rodriguez v. United States, 286 F.3d 972, 980 (7th Cir. 2002). Here, the district court properly denied Mr. Beaven’s proposed amendment on the ground of futility because the Heck doctrine would preclude his conspiracy claim as well.

Mr. Beaven now contends that he should have been allowed to amend his complaint to include other defendants and claims— namely, that prison officials denied him access to the courts by delaying the mailing of his complaint and then transferring him to a more secure unit with less access to the law library. But he has never sought leave to amend his complaint on this ground. We note that Mr. Beaven, a frequent litigator in this circuit, long ago accumulated the three “strikes” allowed prisoners proceeding in forma pauperis by filing frivolous lawsuits and appeals. See 28 U.S.C. § 1915(g); Beaven v. Debruyn, No. 96-3265, 1997 WL 599640 (7th Cir. Sept.25, 1997) (unpublished order). He therefore must pay the full filing fee in order to bring new actions or file new appeals. He will not be permitted to circumvent this restriction by simply amending his complaints to bring new claims after dismissal. We also warn Mr. Beaven that any further frivolous litigation will subject him to monetary fines and a possible bar pursuant to Support Systems Int’l, Inc. v. Mack, 45 F.3d 185, 186 (7th Cir. 1995), forbidding his filing of any further legal papers in any federal court within this circuit except for criminal cases or applications for writs of habeas corpus.

For these reasons, we AFFIRM the district court’s judgment, and DENY Mr. Beaven’s second motion for an injunction pending appeal that he filed on August 4, 2003.