This paper investigates the optimal-cost reachability problem in the context of time Petri nets, where a rate cost is associated with each place. This problem consists in deciding whether or not there exists a sequence of transitions reaching, with minimal cost, a given goal marking. This paper shows that for some subclasses of cost time Petri nets, the optimal-cost reachability problem can be solved more efficiently using a method based on the state classes, without resorting to linear programming or splitting state classes.