To enhance the modeling power of stochastic Petri nets SPNs, new steady-state  analysis methods have been proposed for nets that include non-exponential transitions. Theunderlying stochastic process is a Markov regenerative process MRP when at most one non-exponential transition is enabled in each marking. Time-efficient algorithms for constructing and solving the MRP have been developed. However, the space required to solve such models is often extremely large. This largeness is due to the large number of transitions in the MRP. Traditional analysis methods require that all these transitions be stored in primary memory for efficient computation. If the size of available memory is smaller than that needed to store these transitions, a time-efficient computation is impossible using these methods. To use this class of SPNs to model realistic systems, the space complexity of MRP analysis algorithms must be reduced. In this paper, we propose a new steady-state analysis method that is both time and space efficient. The new method takes advantage of the structure of the underlying process to reduce both computation time and required memory. The performance of the proposed method is compared to existing methods using several SPN examples.