The effects of attention on the responses of visual neurons have been described as a scaling or additive modulation independent of stimulus features and contrast, or as a contrast-dependent modulation. We explored these alternatives by recording neuronal responses in macaque area MT to moving stimuli that evoked similar firing rates but varied in contrast and direction. We presented two identical pairs of stimuli, one inside the neurons' receptive field and the other outside, in the opposite hemifield. One stimulus of each pair always had high contrast and moved in the recorded cell's antipreferred direction (AP pattern), while the other (test pattern) could either move in the cell's preferred direction and vary in contrast, or have the same contrast as the AP pattern and vary in direction. For different stimulus pairs evoking similar responses, switching attention between the two AP patterns, or directing attention from a fixation spot to the AP pattern inside or outside the receptive field, produced a stronger suppression of responses to varying contrast pairs, reaching a maximum ( approximately 20%) at intermediate contrast. For invariable contrast pairs, switching attention from the fixation spot to the AP pattern produced a modulation that ranged from 10% suppression when the test pattern moved in the cells preferred direction to 14% enhancement when it moved in a direction 90 degrees away from that direction. Our results are incompatible with a scaling or additive modulation of MT neurons' response by attention, but support models where spatial and feature-based attention modulate input signals into the area normalization circuit.