Computerized adaptive testing (CAT) has been shown to increase eÆciency in educational measurement. One common application of CAT is to classify students as either pro cient or not proficient in ability. A truncated form of Wald's sequential probability ratio test (SPRT), in which examination is halted after a prespeci ed number of questions, has been proposed to provide a diagnosis of prociency. This article studies the further truncation provided by stochastic curtailment, where an exam is stopped early if completion of the remaining questions would be unlikely to alter the classi cation of the examinee. In a simulation study presented, the increased truncation is shown to offer substantial improvement in test length with only a slight decrease in accuracy.