Upper limb loss is a devastating injury for which current prosthetic replacement inadequately compensates. A lack of wrist movement in prostheses due to mechanical design and control system considerations compels prosthetic users to employ compensatory movements using their upper back and shoulder that can eventually result in strain and overuse injuries. One possible means of easing this control burden is to allow a prosthetic wrist to self-regulate, keeping the terminal device of the prosthesis level relative to the ground when appropriate, such as when raising a cup of liquid. This study aims to outline such a wrist control scheme, and evaluate its function in terms of the effect on compensatory movements, objective system performance, and subjective perception of system performance based on user feedback. To that end, twelve able-bodied participants were recruited to control a body-mounted robotic arm using three different control schemes: fixed-wrist (FW), sequential switching (SS), and automatic levelling (AL). The resulting movement strategies were recorded for two different tasks using 3D motion-capture. SS and AL control schemes induced similar movement strategies and less compensation than FW for horizontal movements, while AL reduced shoulder flexion compared to FW and SS for vertical movements. However, AL was ranked less intuitive and less reliable than the FW. AL and SS both seemed to involve more conscious thought to operate than FW. These results suggest that more complex wrist control schemes may indeed be able to eliminate harmful compensatory movements, but reinforce prior observations that control must be reliable and simple to use or people will opt for an easier system.