The noise inherent in the CNS and the sensorimotor periphery imposes limits on behavioral performance - limits that can only be reached by a controller optimized for the task at hand. I will show that optimal feedback controllers for redundant biomechanical plants exhibit low-rank structure, corresponding to a set of sensorimotor synergies that monitor and control a few task-relevant features of the state. This "minimal intervention" strategy suppresses noise selectively, and predicts larger movement variability in redundant dimensions - in agreement with numerous psychophysical observations. I also will describe a recurrent neural network model of motor cortex, trained to perform sensorimotor transformations given noisy inputs. The network learns to suppress noise selectively - along the task-relevant dimensions of the neural population code. This is reminiscent of a minimal intervention strategy, but uses internal neural feedback rather than sensory feedback.