This work describes how to use reactionless motion control with a free-floating space robot, suggesting thereby some tasks of practical importance. We show that the reactionless motion capability is directly affected by the kinematic structure of the manipulator, depending thereby upon the existence of kinematic redundancy, a typical lower/upper arm subchain and joint offsets. We investigate a seven-DoF redundant manipulator comprising these features and show that approximate reactionless motions can be obtained with the elbow joint only and/or the wrist joints. Using these reactionless motions, we propose three practical maneuvers for eye-in-hand type inspection, arm deploying/stowing and point-to-point motions with partial reactionless motion. Feasibility is verified via numerical simulations.