Visual attention enhances the responses of visual neurons that encode the attended location. Several recent studies have shown that attention also decreases correlations between fluctuations in the responses of pairs of neurons (termed spike count correlation or r(SC)). These results are consistent with two hypotheses. First, attention-related changes in rate and r(SC) might be linked (perhaps through a common mechanism), with attention always decreasing r(SC). Second, attention might either increase or decrease r(SC), possibly depending on the role of the neurons in the behavioral task. We recorded simultaneously from dozens of neurons in area V4 while monkeys performed a discrimination task. We found strong evidence in favor of the second hypothesis, showing that attention can flexibly increase or decrease correlations depending on whether the neurons provide evidence for the same or opposite choices. These results place important constraints on models of the neuronal mechanisms underlying cognitive factors.