This paper describes work we have done on the determination of optimal rocket trajectories which may include singular arcs. In recent years direct collocation and nonlinear programming has proven to be a powerful method for solving optimal control problems. Difficulties in the application of this method can occur if the problem is singular. Techniques exist for solving singular problems indirectly using the associated adjoint equations. Unfortunately, the adjoints are not a part of the direct formulation. In this work we show how adjoint information can be obtained from the direct method to allow the solution of singular problems.