Auditory selective attention is required for parsing crowded acoustic environments, but cortical systems mediating the influence of behavioral state on auditory perception are not well characterized. Previous neurophysiological studies suggest that attention produces a general enhancement of neural responses to important target sounds versus irrelevant distractors. However, behavioral studies suggest that in the presence of masking noise, attention provides a focal suppression of distractors that compete with targets. Here, we compared effects of attention on cortical responses to masking versus non-masking distractors, controlling for effects of listening effort and general task engagement. We recorded single-unit activity from primary auditory cortex (A1) of ferrets during behavior and found that selective attention decreased responses to distractors masking targets in the same spectral band, compared with spectrally distinct distractors. This suppression enhanced neural target detection thresholds, suggesting that limited attention resources serve to focally suppress responses to distractors that interfere with target detection. Changing effort by manipulating target salience consistently modulated spontaneous but not evoked activity. Task engagement and changing effort tended to affect the same neurons, while attention affected an independent population, suggesting that distinct feedback circuits mediate effects of attention and effort in A1.