SummaryThis paper considers the problem of testing for nonzero values of the equicorrelation coefficient of a standard symmetric multivariate normal distribution. Recently, SenGupta (1987) proposed a locally best test. We construct a beta‐optimal test and present selected one and five percent critical values. An empirical power comparison of SenGupta's test with two versions of the beta‐optimal test and the power envelope shows the relative strengths of the three tests. It also allows us to assess and confirm Efron's (1975) rule of when to question the use of a locally best test, at least for this testing problem. On the basis of these results, we argue that the two beta‐optimal tests can be considered as approximately uniformly most powerful tests, at least at the five percent significance