A new manipulation approach, referred to as interleaved continuum-rigid manipulation, which combines inherently safe, flexible actuated segments with more precise embedded rigid-link joints has recently been introduced. The redundantly actuated manipulator possesses the safety characteristics inherent in flexible segment devices while gaining some of the performance attributes of rigid-link joint systems. In this paper, we describe a general controller developed for an interleaved manipulator. The controller is implemented on a clinically-relevant prototype, the results of which demonstrate the advantages of an interleaved manipulator. We also consider kinematic drivers of the interleaved manipulator workspace, showing that careful kinematic considerations can substantially improve manipulator workspace and task accuracy.