Devices, systems, and methods for reconfiguring a surgical manipulator by moving the manipulator within a null-space of a kinematic Jacobian of the manipulator arm. In one aspect, in response to receiving a reconfiguration command, the system drives a first set of joints and calculates velocities of the plurality of joints to be within a null-space. The joints are driven according to the reconfiguration command and the calculated movement so as to maintain a desired state of the end effector or a remote center about which an instrument shaft pivots. In another aspect, the joints are also driven according to a calculated end effector or remote center displacing velocities within a null-perpendicular-space of the Jacobian so as to effect the desired reconfiguration concurrently with a desired movement of the end effector or remote center.