During hands-on cooperative surgery, the use of a redundant robot allows to address encumbrance issues in the Operating Room (OR), which can occur due to the presence of large medical instrumentation, such as the surgical microscope. This work presents a new Null Space Optimization (NSO) strategy to constraint the position of the manipulator’s elbow within predefined range of motions, according to the spatial requirements of the specific procedure, also taking into account the physical joint limits of the robotic assistant. The proposed strategy was applied to the 7 degrees of freedom (dof) lightweight robot LWR4+. The performance of the NSO was compared to two state-of-the-art null space optimization strategies, i.e. damped posture and fixed optimal posture, over a pool of three non-expert users in both strict (20deg) and negligible (100deg) angular encumbrance limitations. The NSO strategy was proved versatile in providing wide elbow mobility together with safe distance from relevant continuity null space boundaries, guaranteeing smooth guidance trajectories. Future works would be performed in order to evaluate the potential feasibility of NSO in a real surgical scenario.