We compared three passive exoskeleton designs in a mock drilling task under three precision requirements levels, defined by required hole sizes, in terms of physical demands (perceived exertion and muscular activation) and quality. The investigated designs were: 1) an upper-body exoskeleton mainly supporting the shoulder; and both 2) full-body, and 3) upper-body exoskeletons, each with connected supernumerary arms. At a fixed pace, participants (n = 12) repeated “drilling” two same-sized holes for 2 min. A fairly consistent result across exoskeleton designs was that higher precision demands increased some muscle activation levels and deteriorated quality. Designs with supernumerary arms led to the largest reductions in quality and increased physical demands overall, mainly in the low back. The shoulder-focused exoskeleton reduced shoulder demands but appeared to reduce quality with the highest precision requirement. Although future work is needed under more diverse/realistic scenarios, these results might be useful to (re)design occupational exoskeletons. •Three passive exoskeleton designs were compared in a simulated overhead task.•Effects of precision demands were fairly consistent across examined designs.•Higher precision demands increased some muscle activations and reduced quality.•Designs with supernumerary arms led to the largest reductions in quality.•Shoulder-focused design reduced quality only with highest precision requirement.