This paper introduces the concepts and procedures of "cognitive conjunction," a new approach to designing and analyzing cognitive activation experiments. Cognitive conjunction compliments categorical approaches such as cognitive subtraction and requires a specific form of statistical inference that involves the conjunction of several hypotheses. While cognitive subtraction studies are designed such that a pair of tasks differ only by the processing component(s) of interest, cognitive conjunction studies are designed such that two or more distinct task pairs each share a common processing difference. The neural correlates of the process of interest are then associated with the common areas of activation for each task pair. There are two main advantages of cognitive conjunction relative to cognitive subtraction. The first is that it provides a greater latitude for selecting baseline tasks because it is not necessary to control for all but the component of interest. The only constraint on selecting the baseline is that the component of interest is the only process that differs in each task pair. The second advantage is that cognitive conjunction does not depend on "pure insertion"--the assumption that the addition of an extra processing component in the activation task has no effect on the implementation of processes that are also engaged by the baseline task. The differences between the design and the statistical analysis of experiments based on cognitive subtraction, cognitive conjunction, and factorial designs are illustrated with a study of phonological retrieval. Cognitive conjunction analysis indicates that irrespective of whether subjects name words, objects, letters, or colors, there is activation of the left posterior basal temporal lobe, the left frontal operculum, the left thalamus, and the midline cerebellum.