An important functional question for understanding how people perform physical actions is to understand how they manipulate objects. Previous research suggests that people prefer to move their hands symmetrically. For bimanual object manipulation, such symmetry may take on several forms, however. Actions may be symmetrical when objects are grasped (start symmetry), when they are placed on their target locations (target symmetry), and/or relative to the objects being moved (object symmetry). We studied how these forms of symmetry influenced grasp selection when participants moved two plungers from two start locations to two target locations. We varied the heights of these locations across conditions. The grasp locations participants adopted indicated a preference for object symmetry. This preference was even stronger when initial symmetry coincided with object symmetry. These results provide a tractable illustration of how multiple planning constraints may interact to give rise to both regularity and flexibility in motor behavior.