To achieve task goals in the various contexts of everyday life, the CNS has to adapt to short time scale changes in the properties of the neuromuscular system, such as those induced by fatigue. Here we investigated how humans preserve task success despite fatigue-induced changes within the neuromuscular system, when they have to aim at a target as fast and as accurately as possible. In such a task, subjects generally choose a compromise between speed and accuracy that has been formalized as Fitts's law. We first characterized the effect of fatigue on Fitts's law in an experiment where participants had to perform fast but accurate elbow movements aimed at targets of different sizes, before and after a fatiguing exercise that reduced maximal voluntary force by approximately 30%. We found that movements were slower to guarantee task success in the presence of fatigue. We then used an optimal control model to determine how fatigue-induced changes in variables such as noise in motor commands, muscle contraction and relaxation times, and the gain between neural activation and muscle force may contribute to changes in Fitts's law with fatigue. We concluded that the observed behavior was not due to the lack of available force, but very likely reflected the fact that the CNS uses the same optimal strategy with a fatigued neuromuscular plant that notably exhibits increased signal-dependent noise in motor commands. This strategy appears necessary to preserve task success in the presence of acute changes in the neuromuscular system.