A mathematical theory and related experimental methodology are developed that permit strong tests of parallel vs serial vs channel summation processing and of exhaustive vs self-terminating processing. We term the basic empirical design the "double factorial paradigm," which is applicable to a variety of cognitive processing situations. The experimental results of an application to a visual detection task provide decisive support for parallel channels with either a self-terminating stopping rule or a coactive summation of information from the two channels. Seriality and exhaustive parallel processing are strongly disconfirmed. The theoretical and empirical findings are discussed in terms of relevant work in the literature.