Multi-stage hypothesis tests are studied as competitors of sequential tests. A class of three-stage tests for the one-dimensional exponential family is shown to be asymptotically efficient, whereas two-stage tests are not. Moreover, in order to be asymptotically optimal, three-stage tests must mimic the behavior of sequential tests. Similar results are obtained for the problem of testing two simple hypotheses.
"Asymptotic Efficiency of Three-Stage Hypothesis Tests." Ann. Statist. 11 (1) 129 - 140, March, 1983. https://doi.org/10.1214/aos/1176346064