Straight-line movements have been studied extensively in the human motor-control literature, but little is known about how to generate curved movements and how to adjust them in a dynamic environment. The present work studied, for the first time to my knowledge, how humans adjust curved hand movements to a target that switches location. Subjects (n = 8) sat in front of a drawing tablet and looked at a screen. They moved a cursor on a curved trajectory (spiral or oval shaped) toward a goal point. In half of the trials, this goal switched 200 ms after movement onset to either one of two alternative positions, and subjects smoothly adjusted their movements to the new goal. To explain this adjustment, we compared three computational models: a superposition of curved and minimum-jerk movements (Flash and Henis in J Cogn Neurosci 3(3):220–230, 1991), Vector Planning (Gordon et al. in Exp Brain Res 99(1):97–111, 1994) adapted to curved movements (Rescale), and a nonlinear dynamical system, which could generate arbitrarily curved smooth movements and had a point attractor at the goal. For each model, we predicted the trajectory adjustment to the target switch by changing only the goal position in the model. As result, the dynamical model could explain the observed switch behavior significantly better than the two alternative models (spiral: P = 0.0002 vs. Flash, P = 0.002 vs. Rescale; oval: P = 0.04 vs. Flash; P values obtained from Wilcoxon test on R ² values). We conclude that generalizing arbitrary hand trajectories to new targets may be explained by switching a single control command, without the need to re-plan or re-optimize the whole movement or superimpose movements.