Humans move in environments with changing accuracy and time demands throughout daily life and in sport. We can readily change our actions to match the demands of a task. Studies have examined the way we plan and prepare voluntary movements so that our actions can match features of a task. We also interact with environments where our movements may be disturbed, such as playing soccer against a defender. Separate studies have used external disturbances to examine flexible, task-dependent changes in sensory processing. Recent theoretical perspectives have suggested that there is an explicit link between the way we perform voluntary actions and how we process sensory feedback. Theory also suggests that we change the way we control our movements in a way that minimizes the consequences of potential errors. However, we do not know how behaviour is tuned to match accuracy constraints under strict time demands, and when there is a potential for actions to be perturbed. Here, we performed two experiments to examine how the nervous system controls upper limb reaching movements with changing accuracy demands and the potential to be disturbed. In Experiment 1, we found that participants reduced the variability of their movements and increased their muscle activity when reaching to small targets. In Experiment 2, participants displayed a reduction in movement variability, while increasing the peak velocity and muscle activity associated with reaching to small targets. When disturbed by the same mechanical perturbations, participants generated larger muscle responses and a reduction in evoked arm motion while reaching to small targets. Overall, our results suggest that participants modify their behaviour to minimize the potential consequences of errors when reaching to small targets. Comparing across Experiments 1 and 2 revealed that participants increased the vigour of their movements when reaching in the presence of perturbations in Experiment 2, but otherwise displayed similar unperturbed reaching behaviour to participants in Experiment 1. Taken together, our results suggest that voluntary actions are modulated to reflect the accuracy demands and potential to be disturbed while performing upper limb reaching movements.