
    John W. HARDING, on behalf of himself and all others similarly situated; and Larry J. Williams, on behalf of himself and all others similarly situated; Robert A. Goff, Appellants, v. UNITED STATES POSTAL SERVICE, John W. Ross and Albert Evans, Postmasters, Charleston, West Virginia, Walter A. Krankemann, Director of Employee and Labor Relations, United States Postal Service, Charleston; Keith C. Austin and T.J. Johnson, Postmasters, St. Albans; American Postal Workers Union (AFL-CIO); and The National Post Office Mail Handlers Union, Appellees.
    No. 85-2115.
    United States Court of Appeals, Fourth Circuit.
    Argued May 7, 1986.
    Decided Oct. 9, 1986.
    
      Richard L. Withers, Charleston, W.Va., for appellants.
    E. Roy Hawkens, Appellate Staff, Civil Div., Dept. of Justice (Richard K. Willard, Asst. Atty. Gen., Washington, D.C., David A. Faber, U.S. Atty., Charleston, W.Va., Stephen E. Alpern, Associate Gen. Counsel, Karen A. Intrater, Office of Labor Law, U.S. Postal Service, John F. Cordes, Washington, D.C., on brief), for appellees.
    Before WIDENER, HALL and CHAPMAN, Circuit Judges.
   WIDENER, Circuit Judge:

John W. Harding, Larry J. Williams and Robert A. Goff appeal from an order of the district court, 618 F.Supp. 1330 (1985), dismissing their civil action against the United States Postal Service and several of its employees. Finding no merit to their claims, we affirm.

In this case, the appellants are all former employees of the postal service and all challenge their discharge from employment. Harding was discharged from his position as a clerk for the postal service on December 28, 1981 for wilfully filing a false injury compensation claim. Harding unsuccessfully filed a grievance challenging his discharge. That discharge was upheld in arbitration on November 2, 1982. Goff was also discharged from his position as a clerk with the postal service for filing a false injury compensation claim. Goff's discharge was upheld following arbitration. Williams was discharged from the postal service on December 15, 1981 for “failure to meet the arduous physical requirements of [his] mail handler position.” Williams had previously been accused by the postal service of filing a false injury compensation claim. Williams’ discharge was upheld following arbitration.

The appellants then filed this suit primarily claiming that their constitutional rights to due process as set out in Bivens v. Six Unknown Named Agents of Federal Bureau of Narcotics, 403 U.S. 388, 91 S.Ct. 1999, 29 L.Ed.2d 619 (1971), were violated because the postal service labeled their compensation claims as fraudulent and that such a label adversely affected all the proceedings and investigations conducted by the postal service. Appellants also claim that they were the subject of abusive discharges under state law.

The district court dismissed appellants’ Bivens claim, concluding that such a constitutional remedy is not available to these appellants because they had other procedures available to them to seek redress of their claims. These appellants arbitrated their claims under the final and binding provisions of their union’s collective bargaining agreement. As well, they had available the detailed administrative remedies under 5 U.S.C. § 7501, et seq. Under Bush v. Lucas, 462 U.S. 367, 103 S.Ct. 2404, 76 L.Ed.2d 648 (1983), they cannot now seek to bring a private cause of action directly against the postal service for such alleged constitutional violations connected with their discharges.

We have considered the appellants’ remaining claims of error and find them to be without merit.

Accordingly, the judgment of the district court is

AFFIRMED. 
      
      . The appellants originally named the American Postal Workers’ Union and the National Post Office Mail Handlers’ Union as defendants.
      They have since settled their claims with these unions and do not include any claims against the unions in their appeal.
     