Sequential mastery testing (SMT) has been researched as an efficient alternative to paper-and-pencil testing for pass/fail examinations. One popular method for determining when to cease examination in SMT is the truncated sequential probability ratio test (TSPRT). This article introduces the application of stochastic curtailment in SMT to shorten the TSPRT without substantially compromising error rates. Unlike the TSPRT, the stochastically curtailed procedure exhibits an optimality property known as weak admissibility. Error bounds of the two methods are provided in terms of one another. In two simulation sets, the stochastically curtailed procedure considerably improved the average test length of an SMT with only a slight decrease in accuracy. (Contains 3 tables.)