An approach to simulating models of highly dependable systems with general failure and repair time distributions is described. The approach combines importance sampling with event rescheduling in order to obtain variance reduction in such rare event simulations. The approach is general in nature and allows effective simulation of a variety of features commonly arising in dependability modeling. For example, it is shown how the technique can be applied to systems with periodic maintenance. The effects on the steady-state availability of the maintenance period and of different failure time distributions are explored. Some of the trade-offs involved in the design of specific rescheduling rules are described, and their potential effectiveness in simulations of systems with nonexponential failure and repair time distributions are demonstrated. It is found that an effective method for selecting the rescheduling distribution is to keep the probability of a failure transition in the range between 0.1 and 0.5.