If sensorineural systems are efficient, redundancy should be extracted to optimize information processing. Stilp et al. reported efficient coding of a robust correlation (r2 = 0.95) among complex acoustic attributes following passive exposure [J. Acoust. Soc. Am. 124, 2493 (2008)] and through continuous active testing [J. Acoust. Soc. Am. 126, 2203–2204 (2009)]. Across studies, discrimination of differences between sounds orthogonal to the correlation is initially poor relative to sounds consistent with the correlation. Only following continued testing, listeners discovered variance inconsistent with the correlation, and discrimination of orthogonal sounds improved. Present studies examine how strong a correlation must be to create these perceptual changes. Listeners discriminated stimuli (AXB) for which the correlation between two complex independent dimensions, attack/decay (AD) and spectral shape (SS), varied. Poorer discrimination of differences that do not respect the correlation persists when the range over which AD/SS covary is truncated (r2 = 0.65), and when orthogonal sounds are modestly oversampled (r2 = 0.89). When correlations are decreased by extreme oversampling of orthogonal sounds (r2 = 0.69) or addition of orthogonal sounds with more extreme values (r2 = 0.69), effects diminish. Connectionist models employing principal components analysis consistently predict listener performance across experiments. [Work supported by NIDCD.]