Stochastic programs are said to have simple recourse if the state vector in each period is uniquely determined once all previous decision and random vectors are known. This paper considers two period problems of this nature. Conditions are presented that ensure that there is an equivalent deterministic convex program that has a continuously differentiable objective function. This leads to the development of a primal feasible direction algorithm. Relatively easily calculated bounds on the optimal objective value are presented. Several special cases are discussed that lead to simpler solutions. Two financial planning examples are considered; for one of them it is appropriate to consider a bisecting algorithm.