Optimal feedback control postulates that feedback responses depend on the task relevance of any perturbations. We test this prediction in a bimanual task, conceptually similar to balancing a laden tray, in which each hand could be perturbed up or down. Single-limb mechanical perturbations produced long-latency reflex responses ("rapid motor responses") in the contralateral limb of appropriate direction and magnitude to maintain the tray horizontal. During bimanual perturbations, rapid motor responses modulated appropriately depending on the extent to which perturbations affected tray orientation. Specifically, despite receiving the same mechanical perturbation causing muscle stretch, the strongest responses were produced when the contralateral arm was perturbed in the opposite direction (large tray tilt) rather than in the same direction or not perturbed at all. Rapid responses from shortening extensors depended on a nonlinear summation of the sensory information from the arms, with the response to a bimanual same-direction perturbation (orientation maintained) being less than the sum of the component unimanual perturbations (task relevant). We conclude that task-dependent tuning of reflexes can be modulated online within a single trial based on a complex interaction across the arms.