Paying attention to a sensory feature improves its perception and impairs that of others. Recent work has shown that a Normalization Model of Attention (NMoA) can account for a wide range of physiological findings and the influence of different attentional manipulations on visual performance. A key prediction of the NMoA is that attention to a visual feature like an orientation or a motion direction will increase the response of neurons preferring the attended feature (response gain) rather than increase the sensory input strength of the attended stimulus (input gain). This effect of feature-based attention on neuronal responses should translate to similar patterns of improvement in behavioral performance, with psychometric functions showing response gain rather than input gain when attention is directed to the task-relevant feature. In contrast, we report here that when human subjects are cued to attend to one of two motion directions in a transparent motion display, attentional effects manifest as a combination of input and response gain. Further, the impact on input gain is greater when attention is directed towards a narrow range of motion directions than when it is directed towards a broad range. These results are captured by an extended NMoA, which either includes a stimulus-independent attentional contribution to normalization or utilizes direction-tuned normalization. The proposed extensions are consistent with the feature-similarity gain model of attention and the attentional modulation in extrastriate area MT, where neuronal responses are enhanced and suppressed by attention to preferred and non-preferred motion directions respectively.