               IN THE UNITED STATES COURT OF APPEALS
                       FOR THE FIFTH CIRCUIT
                         __________________

                            No. 95-20475
                        Conference Calendar
                         __________________

MICHAEL DWYER MCCULLOUGH,

                                       Plaintiff-Appellant,
versus

TEXAS DEPARTMENT OF CRIMINAL JUSTICE -
INSTITUTIONAL DIVISION,

                                       Defendant-Appellee.

                        - - - - - - - - - -
           Appeal from the United States District Court
                for the Southern District of Texas
                       USDC No. CA H-93-2709
                        - - - - - - - - - -
                         (October 18, 1995)
Before POLITZ, Chief Judge, and REAVLEY and SMITH, Circuit Judges.

PER CURIAM:*

     Michael Dwyer McCullough filed a pro se civil rights

complaint, 42 U.S.C. § 1983, against the Texas Department of

Criminal Justice - Institutional Division alleging that he was

improperly denied good-time credits.    The district court

dismissed the complaint as barred by the Eleventh Amendment.

McCullough filed a timely notice of appeal from the judgment and

a Rule 60(b) motion.   The district court denied the Rule 60(b)

motion because any § 1983 claim was premature under Heck v.

Humphrey, 114 S.Ct. 2364 (1994).


     *
          Local Rule 47.5 provides: "The publication of opinions
that have no precedential value and merely decide particular
cases on the basis of well-settled principles of law imposes
needless expense on the public and burdens on the legal
profession." Pursuant to that Rule, the court has determined
that this opinion should not be published.
                             No. 95-20475
                                  -2-

     The district court should permit a pro se plaintiff to amend

a complaint if it appears that there is a potential ground for

relief, see Gallegos v. La. Code of Criminal Procedures Art. 658,

858 F.2d 1091, 1092 (5th Cir. 1988), but the district court need

not permit futile amendments.    See Davis v. Louisiana State

Univ., 876 F.2d 412, 413-14 (5th Cir. 1989).    McCullough's claim

is not cognizable under § 1983; the district court properly

dismissed the complaint.    Heck, 114 S. Ct. at 2372.

     McCullough's argument that the district court improperly

dismissed the complaint as barred by the Eleventh Amendment need

not be addressed.   McCullough's claim is not cognizable under

Heck, and the judgment is affirmed on this alternative ground.

See Sojourner T. v. Edwards, 974 F.2d 27, 30 (5th Cir. 1992),

cert. denied, 113 S. Ct. 1414 (1993).

     McCullough did not file a notice of appeal after the

district court denied his Rule 60(b) motion; this court does not

have jurisdiction over the order denying the motion.     McKethan v.

Texas Farm Bureau, 996 F.2d 734, 744 (5th Cir. 1993), cert.

denied, 114 S. Ct. 694 (1994).

     We caution McCullough that any additional frivolous appeals

filed by him or on his behalf will invite the imposition of

sanctions.   To avoid sanctions, McCullough is further cautioned

to review all pending appeals to ensure that they do not raise

arguments that are frivolous because they have been previously

decided by this court.

     Appeal DISMISSED.     Howard v. King, 707 F.2d 215, 219-20 (5th

Cir. 1983); 5th Cir. R. 42.2.
