This study investigated the use of motor abundance during the transport and placing of objects that required either precise or minimal orientation to the target. Analyses across repetitions of the structure of joint configuration variance relative to the position and orientation constraints were performed using the Uncontrolled Manifold (UCM) approach. Results indicated that the orientation constraint did not affect stability of the hand’s spatial path. Orientation was weakly stabilized during the late transport phase independent of the orientation constraint, indicating no default synergy stabilizing orientation. Stabilization of orientation for conditions most requiring it for successful insertion of the object was present primarily during the adjustment phase. The results support the hypothesis that a major advantage of a control scheme that utilizes motor abundance is the ability to resolve multiple task constraints simultaneously without undue interference among them.