In digital imaging systems it is often necessary to reduce the bit precision of an image due to limitations in transmission or storage. The 8 bit storage of a 12 bit medical image is a good example. Generally, the input images are linearly quantized, and the goal is to find the fixed, digital mapping that preserves the highest image quality at the reduced bit precision. Since the response of the visual system to brightness differences is nonlinear, the optimal mapping is nonlinear. The traditional approach is to use one of the commonly accepted models of the visual system, e.g. a logarithm or power-law, to construct a Look-Up-Table (LUT) that performs the digital mapping. This paper will demonstrate that this approach is visually suboptimal for finite input precision, even if the visual model is perfect. A better method for constructing the digital mapping or LUT will be derived by posing the problem as a combinational optimization problem of taking N bits from M bits, where N is less than M, such that a visual distortion metric is minimized. Computer generated images will be used to demonstrate the method in a 12 bit to 8 bit application, and a 6 bit to 2 bit example will be included to illustrate its convergence characteristics.