Noise correlations (r(noise)) between neurons can affect a neural population's discrimination capacity, even without changes in mean firing rates of neurons. r(noise), the degree to which the response variability of a pair of neurons is correlated, has been shown to change with attention with most reports showing a reduction in r(noise). However, the effect of reducing r(noise) on sensory discrimination depends on many factors, including the tuning similarity, or tuning correlation (r(tuning)), between the pair. Theoretically, reducing r(noise) should enhance sensory discrimination when the pair exhibits similar tuning, but should impair discrimination when tuning is dissimilar. We recorded from pairs of neurons in primary auditory cortex (A1) under two conditions: while rhesus macaque monkeys (Macaca mulatta) actively performed a threshold amplitude modulation (AM) detection task and while they sat passively awake. We report that, for pairs with similar AM tuning, average r(noise) in A1 decreases when the animal performs the AM detection task compared with when sitting passively. For pairs with dissimilar tuning, the average r(noise) did not significantly change between conditions. This suggests that attention-related modulation can target selective subcircuits to decorrelate noise. These results demonstrate that engagement in an auditory task enhances population coding in primary auditory cortex by selectively reducing deleterious r(noise) and leaving beneficial r(noise) intact.