This paper presents an algorithm for designing spacecraft reconfiguration maneuvers, which is a difficult 6 DOF trajectory design problem with nonlinear attitude dynamics and non-convex constraints. In addition, some of the constraints couple the positions and attitudes of the spacecraft, which makes the problems high-dimensional. The essential feature of the design methodology is the separation into a simplified path planning problem obtaining a feasible solution, then improving it significantly by a smoothing operation. The first step is solved using a rapidly-exploring random tree. The smoother then optimizes the trajectories by iteratively solving a linear program using a linearization of the cost function, dynamics, and constraints about the initial feasible solution. Examples are presented to demonstrate the validity of the approach for complex problems with four spacecraft.