If the purpose of adaptation is to fit sensory systems to different environments, it may implement an optimization of the system. What the optimum is depends on the statistics of these environments. Therefore, the system should update its parameters as the environment changes. A Kalman-filtering strategy performs such an update optimally by combining current estimations of the environment with those from the past. We investigate whether the visual system uses such a strategy for speed adaptation. We performed a matching-speed experiment to evaluate the time course of adaptation to an abrupt velocity change. Experimental results are in agreement with Kalman-modeling predictions for speed adaptation. When subjects adapt to a low speed and it suddenly increases, the time course of adaptation presents two phases, namely, a rapid decrease of perceived speed followed by a slower phase. In contrast, when speed changes from fast to slow, adaptation presents a single phase. In the Kalman-model simulations, this asymmetry is due to the prevalence of low speeds in natural images. However, this asymmetry disappears both experimentally and in simulations when the adapting stimulus is noisy. In both transitions, adaptation now occurs in a single phase. Finally, the model also predicts the change in sensitivity to speed discrimination produced by the adaptation.