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A key computation underlying perceptual decisions is the temporal integration of "evidence" in favor of different states of the world. Studies from psychology and neuroscience have shown that observers integrate multiple samples of noisy perceptual evidence over time toward a decision [1–11]. An influential model posits perfect evidence integration (i.e., without forgetting), enabling optimal decisions based on stationary evidence [2, 3, 12]. However, in real-life environments, the perceptual evidence typically changes continuously. We used a computational model to show that, under such conditions, performance can be improved by means of leaky (forgetful) integration, if the integration timescale is adapted toward the predominant signal duration. We then tested whether human observers employ such an adaptive integration process. Observers had to detect visual luminance "signals" of variable strength, duration …