We present a method to maintain the subjective perception of volume of audio signals and, at the same time, reduce their absolute peak value. We focus on achieving this without compromising the perceived audio quality. This is specially useful, for example, to maximize the perceived reproduction level of loudspeakers where simply amplifying the signal amplitude, and hence their peak value, is limited due to already constrained physical designs. In particular, we minimize the absolute peak value subject to a constraint based on auditory masking. This limits the perceptual difference between the original and the modified signals. Moreover, this constraint can be tuned and allows to control the resulting audio quality. We show results comparing loudness and audio quality as a function of peak reduction. These results suggest that our method presents the best trade-off between loudness and audio quality when compared against classical methods based on compression and clipping.