Jolly (1982, Biometrics 38, 301-321) presented modifications of the Jolly-Seber model for capture-recapture data, which assume constant survival and/or capture rates. Where appropriate, because of the reduced number of parameters, these models lead to more efficient estimators than the Jolly-Seber model. The tests to compare models given by Jolly do not make complete use of the data, and we present here the appropriate modifications, and also indicate how to carry out goodness-of-fit tests which utilize individual capture history information. We also describe analogous models for the case where young and adult animals are tagged. The availability of computer programs to perform the analysis is noted, and examples are given using output from these programs.