We consider classes of stochastic linear programming problems which can be efficiently solved by deterministic algorithms. For two–stage recourse problems we identify two such classes. The first one consists of problems where the number of stochastically independent random variables is relatively low; the second class is the class of simple recourse problems. The proposed deterministic algorithm is successive discrete approximation. We also illustrate the impact of required accuracy on the efficiency of this algorithm. For jointly chance constrained problems with a random right–hand–side and multivariate normal distribution we demonstrate the increase in efficiency when lower accuracy is required, for a central cutting plane method. We support our argumentation and findings with computational results.