It is shown that for a test of a composite hypothesis on the parameter $\theta$ of an exponential family of distributions, mixture stopping rules are almost optimal with respect to certain criteria of optimality and a unique stopping rule is to be found among them which is optimal with respect to another type of optimality.
"Optimality and Almost Optimality of Mixture Stopping Rules." Ann. Statist. 6 (4) 910 - 916, July, 1978. https://doi.org/10.1214/aos/1176344264