In the redundant signals task, participants respond, in the same way, to stimuli of several sources, which are presented either alone or in combination (redundant signals). The responses to the redundant signals are typically much faster than to the single signals. Several models explain this effect, including race and coactivation models of information processing. Race models assume separate channels for the two components of a redundant signal, with the response time determined by the faster of the two channels. Because the slower processing times in one channel are cancelled out by faster processing in the other channel, responses to redundant signals are, on average, faster than to single signals. In contrast, coactivation models relate the redundancy gain to some kind of integrated processing of the redundant information. The two models can be distinguished using the race model inequality (Miller, 1982, Cognitive Psychology, 14, 247–279) on the response time distribution functions. Miller’s prediction was derived for experiments with 100% accuracy, and despite corrections for guesses and omitted responses, it is limited to easy tasks with negligible error rates. In this article we generalize Miller’s inequality to non-trivial experimental tasks in which incorrect responses may occur systematically. The method is illustrated using data from a difficult discrimination task with choice responses.