Attention is believed to enhance perception by altering the activity-level correlations between pairs of neurons. How attention changes neuronal activity correlations is unknown. Using multielectrodes in monkey visual cortex, we measured spike-count correlations when single or multiple stimuli were presented and when stimuli were attended or unattended. When stimuli were unattended, adding a suppressive, nonpreferred stimulus beside a preferred stimulus increased spike-count correlations between pairs of similarly tuned neurons but decreased spike-count correlations between pairs of oppositely tuned neurons. A stochastic normalization model containing populations of oppositely tuned, mutually suppressive neurons explains these changes and also explains why attention decreased or increased correlations: as an indirect consequence of attention-related changes in the inputs to normalization mechanisms. Our findings link normalization mechanisms to correlated neuronal activity and attention, showing that normalization mechanisms shape response correlations and that these correlations change when attention biases normalization mechanisms.