Weber's law--constancy of the coefficient of variation--is an apparently ubiquitous feature of time perception, and forms the foundation of several theories of timing. We sought evidence for Weber's law in temporal production and categorization experiments. The production task required pigeons to switch between keys within a specified temporal window. The categorization task required them to classify a stimulus duration as either short or long. Weber fractions did not descend to a horizontal asymptote, but were U-shaped: they decreased as a function of target duration, and increased again at intermediate and long durations. This pattern conforms neither to Weber's law, nor to its generalized form (Getty, D.J., 1975. Discrimination of short temporal intervals: a comparison of two models. Percept. Psychophys. 18, 1-8). A model of counter failure accommodated the U-shaped pattern.