Cytokinesis and other cell shape changes are driven by the actomyosin contractile cytoskeleton.The molecular rearrangements that bring about contractility in non-muscle cells are currently debated. Specifically, both filament sliding by myosin motors, as well as cytoskeletal crosslinking by myosins and non-motor crosslinkers, are thought to promote contractility. Here, we examined how the abundance of motor and non-motor crosslinkers controls the speed of cytokinetic furrowing. We built a minimal model to simulate the contractile dynamics of the C. elegans zygote cytokinetic ring. This model predicted that intermediate levels of non-motor crosslinkers would allow maximal contraction speed, which we found to be the case for the scaffold protein anillin, in vivo. Our model also demonstrated a non-linear relationship between the abundance of motor ensembles and contraction speed. In vivo, thorough depletion of non-muscle myosin II delayed furrow initiation, slowed F-actin alignment, and reduced maximum contraction speed, but partial depletion allowed faster-than-expected kinetics. Thus, both motor and non-motor crosslinkers promote cytokinetic ring closure when present at low levels, but act as a brake when present at higher levels. Together, our findings extend the growing appreciation for the roles of crosslinkers, but reveal that they not only drive but also brake cytoskeletal remodeling.