Do Ss always process multidimensional stimuli according to psychologically primary dimensions? Our hypothesis is that they do: Primary dimensions provide one component of a new model of dimensional interaction, a model that distinguishes information processed at the level of attributes from information processed at the level of the stimulus. By using sound stimuli created from the dimensions pitch-loudness (Experiments 1 and 2), pitch-timbre (Experiment 3), and loudness-timbre (Experiment 4), we tested performance in selective- and divided-attention tasks at each of three orientations of axes: 0 degrees, 22.5 degrees, and 45 degrees. Each experiment revealed strong evidence of primacy: As axes rotated from 0 degrees to 45 degrees, selective attention deteriorated, but divided attention improved, producing a distinct pattern of convergence. Each experiment also revealed effects of congruity: Attributes from corresponding poles of a dimension (e.g., high pitch and loud) were classified faster than those from noncorresponding poles. The results fit well with our new conception but are inconsistent with other current models of dimensional interaction.