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To press a button, a finger must push down and pull up with the right force and timing. How the motor system succeeds in button-pressing, in spite of neural noise and lacking direct access to the mechanism of the button, is poorly understood. This paper investigates a unifying account based on neurome- chanics. Mechanics is used to model muscles controlling the finger that contacts the button. Neurocognitive principles are used to model how the motor system learns appropriate muscle activations over repeated strokes though relying on degraded sensory feedback. Neuromechanical simulations yield a rich set of predictions for kinematics, dynamics, and user performance and may aid in understanding and improving input devices. We present a computational implementation and evaluate predictions for common button types.