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The optimum sequential detector for two-hypotheses problems when both hypotheses are simple is a likelihood ratio processor in tandem with the optimum stopping rule. When one of the two hypotheses is composite, the optimum detector consists of a likelihood ratio processor, an optimum stopping rule, and an updating processor on the distributed parameters of the composite hypothesis. Discussed is a general theory for obtaining the optimum sequential detector for a composite hypothesis when the available observation length is finite. The general theory is applied to the problem of a signal of unknown amplitude to obtain the optimum receiver design and its evaluation. Limited numerical results indicate the deferred-decision detector is better than the comparable fixed-time detector because it makes terminal decisions of better quality as opposed to making terminal decisions of the same quality in a shorter time.