Rapid and reliable robot bin picking is a critical challenge in automating warehouses, often measured in picks-per-hour (PPH). We explore increasing PPH using faster motions based on optimizing over a set of candidate grasps. The source of this set of grasps is two-fold: (1) grasp-analysis tools such as Dex-Net generate multiple candidate grasps, and (2) each of these grasps has a degree of freedom about which a robot gripper can rotate. In this paper, we present Grasp-Optimized Motion Planning (GOMP), an algorithm that speeds up the execution of a bin picking robot’s operations by incorporating robot dynamics and a set of candidate grasps produced by a grasp planner into an optimizing motion planner. We compute motions by optimizing with sequential quadratic programming (SQP) and iteratively updating trust regions to account for the non-convex nature of the problem. In our formulation, we constrain the motion to remain within the mechanical limits of the robot while avoiding obstacles. We further convert the problem to a time-minimization by repeatedly shorting a time horizon of a trajectory until the SQP is infeasible. In experiments with a UR5, GOMP achieves a speed up of 9x over a baseline planner.