A general technique for computing optimal state transition probabilities for software tests, based on a Markov usage model, is developed. The optimization criterion is maximum precision of unbiased dependability estimates derived from the test results. Three different dependability measures are considered: (i) risk, (ii) safety, and (iii) reliability. As input, pre-information on failure probabilities and losses in case of failure related with single operations is used. The optimization itself is done by means of a numerical procedure which is fast because of the convexity of the underlying stochastic optimization problem. The procedure can be improved by the construction of a distribution with a common lower bound on state transition probabilities; this distribution may also be used in the more general context of structural statistical testing of software.