This paper considers some methods for reducing the number of significance tests undertaken when analyzing and reporting results of clinical trials. Emphasis is placed on designing and analyzing clinical trials to examine a composite hypothesis concerning multiple endpoints and combining this multiple endpoint methodology with group sequential methodology. Four methods for composite hypotheses are considered: an ordinary least squares and a generalized least squares approach both due to O'Brien (1984, Biometrics 40, 1079-1087), a new modification of these, and an approximate likelihood ratio test, due to Tang, Gnecco, and Geller (1989, Biometrika 76, 577-583). These are extended for group sequential use. In particular, simulation is used to generate critical values and sequences of nominal significance levels for the approximate likelihood ratio test, which is not normally distributed. An example is given and the relative merits of the suggested approaches are discussed.