This dissertation considers efficient developmental testing for one-shot systems (for example, missiles) that are destroyed in testing or first normal use, where there is the possibility of "reliability growth" of the basic system design as a result of redesigns following failed developmental tests. We consider situations where the cost of redesign is negligible and there is a fixed procurement budget covering both system development and purchase, each developmental test produces either a binary (success-failure) or a continuous outcome. The analysis offered here is intended as an answer to the question "How much testing is enough?" posed by Seglie (1992) in the context of the procurement of military weapons systems. For a particular two-state model of system reliability, dynamic programming is used to identify testing plans/stopping rules that are optimal in the sense of maximizing the expected number of effective systems (of the final design) that can be purchased with the remaining budget when developmental testing is terminated. Several reasonable and easily implemented sub-optimal rules are also considered, and their performances are compared to that of the optimal rule for a variety of combinations of model parameters.