In this paper a new algorithm for the transient solution of a sub-class of Deterministic Stochastic Petri Nets (DSPN) is proposed. The technique can be applied to DSPNs comprising only deterministic and immediate transitions and such that in each tangible marking only one deterministic transition is enabled. The algorithm does not require any additional restriction on the deterministic transition delays that can have any positive real value. Most of the optimized algorithms presented in the literature are based on an efficient solution of the equations governing the stochastic process associated with the DSPN; the new algorithm we propose is based on an efficient combinatorial analysis of the paths within the state space underlying the DSPN, instead.