A large number of recent studies suggest that the sensorimotor system employs probabilistic models to predict its environment and makes inferences about unobserved variables in line with Bayesian statistics. One of the important features of Bayesian statistics is Occam's Razor - an inbuilt preference for simpler models when comparing competing models that explain some observed data equally well. Here we test directly for Occam's Razor in sensorimotor control. We designed a sensorimotor task, where participants had to draw lines through clouds of noisy samples of an unobserved curve generated by one of two possible probabilistic models - a simple model with a large length scale, leading to smooth curves and a complex model with a short length scale, leading to more wiggly curves. In training trials participants were informed about the model that generated the stimulus so that they could learn the statistics of each model. In probe trials participants were then exposed to ambiguous stimuli. In probe trials where the ambiguous stimulus could be fit equally well by both models, we found that participants showed a clear preference for the simpler model. Moreover, we found that participants' choice behavior was quantitatively consistent with Bayesian Occam's Razor. We could also show that participants' drawn trajectories were similar to samples from the Bayesian predictive distribution over trajectories and significantly different from two non-probabilistic heuristics. In two control experiments, we show that the preference of the simpler model cannot be simply explained by a difference in physical effort or by a preference for curve smoothness. Our results suggest that Occam's Razor is a general behavioral principle already present during sensorimotor processing.