Six experiments investigated how variability on irrelevant stimulus dimensions and variability on response dimensions contribute to spatial and nonspatial stimulus-response (S-R) correspondence effects. Experiments 1-3 showed that, when stimuli varied in location and number, S-R correspondence effects for location or numerosity occurred when responses varied on these dimensions but not when responses were invariant on these dimensions. These results are consistent with the response-discrimination account, according to which S-R correspondence effects should only arise for a dimension that is used for discriminating between responses in working memory. Experiments 4-6 showed that, when responses varied in location and number, both invariant and variable stimulus number produced correspondence effects in S-R numerosity. In summary, the present results indicate that the usefulness of a particular dimension for response discrimination can be sufficient for producing S-R correspondence effects, whereas variability of a stimulus dimension is not sufficient for producing such effects.