Performance on selective-attention and divided-attention tasks shows strong and consistent interactions when participants rapidly classify auditory stimuli whose linguistic and perceptual dimensions (the words low vs. high, low and high pitch, low and high position in space) share common labels. Compared with baseline performance, response times were greater when one or two irrelevant dimensions varied (Garner interference) and when combinations of attributes were incongruent rather than congruent (congruence effects). Performance depended only on the congruence relationships between the relevant dimension and each of the irrelevant dimensions and not on the congruence relationships between the irrelevant dimensions themselves. In selective attention, an additive multidimensional model accounts well for the patterns of both Garner interference and congruence effects.