We study the stochastic resource-constrained project scheduling problem or SRCPSP, where project activities have stochastic durations. A solution is a scheduling policy, and we propose a new class of policies that is a generalization of most of the classes described in the literature. A policy in this new class makes a number of a priori decisions in a preprocessing phase, while the remaining scheduling decisions are made online. A two-phase local search algorithm is proposed to optimize within the class. Our computational results show that the algorithm has been efficiently tuned toward finding high-quality solutions and that it outperforms all existing algorithms for large instances. The results also indicate that the optimality gap even within the larger class of elementary policies is very small.