Subtractive dither is a technique which may be used to reduce the occurrence of compression artifacts from near-lossless compression. Standard subtractive dither incurs a cost, however, in the form of an increase in rate and distortion, and by giving the reconstructed signal an overall grainy appearance. It is possible to compromise between the costs and benefits of dithering by using dither signals which tend to take on smaller values than the standard dither signal. For reasonable cost and benefit metrics, the optimal dither signals are shown to be those which are uniform on intervals of the form [-k/2,k/2], where k/spl epsiv/[0,q] and q is the quantization step size. Additional results are given under more general assumptions.