The structure of joint angle variability and its changes with practice were investigated using the uncontrolled manifold (UCM) computational approach. Subjects performed fast and accurate bimanual pointing movements in 3D space, trying to match the tip of a pointer, held in the right hand, with the tip of one of three different targets, held in the left hand during a pre-test, several practice sessions and a post-test. The prediction of the UCM approach about the structuring of joint angle variance for selective stabilization of important task variables was tested with respect to selective stabilization of time series of the vectorial distance between the pointer and aimed target tips (bimanual control hypothesis) and with respect to selective stabilization of the endpoint trajectory of each arm (unimanual control hypothesis). The components of the total joint angle variance not affecting (V(COMP)) and affecting (V(UN)) the value of a selected task variable were computed for each 10% of the normalized movement time. The ratio of these two components R(V)=V(COMP)/V(UN) served as a quantitative index of selective stabilization. Both the bimanual and unimanual control hypotheses were supported, however the R(V) values for the bimanual hypothesis were significantly higher than those for the unimanual hypothesis applied to the left and right arm both prior to and after practice. This suggests that the CNS stabilizes the relative trajectory of one endpoint with respect to the other more than it stabilizes the trajectories of each of the endpoints in the external space. Practice-associated improvement in both movement speed and accuracy was accompanied by counter-intuitive lack of changes in R(V). Both V(COMP) and V(UN) variance components decreased such that their ratio remained constant prior to and after practice. We conclude that the UCM approach offers a unique and under-explored opportunity to track changes in the organization of multi-effector systems with practice and allows quantitative assessment of the degree of stabilization of selected performance variables.