This study used the uncontrolled manifold (UCM) approach to study joint coordination underlying the control of task-related variables important for success at reaching and pointing to targets. More combinations of joint motions are available to the control system to achieve task success than are strictly necessary. How this abundance of motor solutions is managed by the nervous system and whether and how the availability of visual information affects the solution to joint coordination was investigated in this study. The variability of joint angle combinations was partitioned into 2 components with respect to control of either the hand's path or the path of the arm's center of mass (CM). The goal-equivalent variability (GEV) component represents trial-to-trial fluctuations of the joint configuration consistent with a stable value of the hand or CM path. The other component, non-goal-equivalent variability (NGEV), led to deviations away from the desired hand or CM path. We hypothesized a style of control in which the NGEV component is selectively restricted while allowing a range of goal-equivalent joint combinations to be used to achieve stability of the hand and CM paths. Twelve healthy right-handed subjects reached across their body to the center of a circular target with both the right and left arms and with their eyes open or closed on different trials. When repeating the task with the same arm under identical task conditions, subjects used a range of goal-equivalent joint configurations to control the entire trajectory of both the hand's and the arm's CM motion, as well as the terminal position of the pointer-tip. Overall joint configuration variability was consistently larger in the middle of the movement, near the time of peak velocity. The style of joint coordination was qualitatively similar regardless of the arm used to point or the visual condition. Quantitative differences in the structure of joint coordination were present for the non-dominant arm, however, when pointing in the absence of vision of the hand and target. The results of this study suggest that the nervous system uses a control strategy that provides for a range of goal-equivalent, rather than unique, joint combinations to stabilize the values of important task-related variables, while selectively restricting joint configurations that change these values. The possible advantage of this style of control is discussed. Absence of vision during reaching affected joint coordination only quantitatively and only for the less skilled left arm, suggesting that the role of visual information may be greater when organizing the motor components of this arm.