In testing one hypothesis against another, observations may be obtained sequentially. The special feature of the situation considered in this paper is that after the decision to stop observation is made a fixed number of additional observations are available for the terminal decision. The test is then based on the ratio of the likelihoods (at two simple hypotheses) of all the observations (whatever stopping rule is used). Numerical comparisons are made for various cases when the hypotheses concern the mean of a normal distribution with the variance known; these cases include a fixed-sample-size procedure as well as cases where several numbers of additional observations are available after the Wald sequential probability ratio test is used as a stopping rule.