1. A method for modifying an input digital image having an (x,y) array of image pixels, each image pixel having an input code value for each of four or more color channels, to produce a depleted digital image having depleted code values that substantially preserve perceived color and which are subject to a total colorant amount limit, comprising the steps of: a) determining an input perceived color corresponding to the input code values using a device color model; b) determining an input colorant amount for each color channel in response to the corresponding input code value and a colorant amount function that relates the input code value to the colorant amount for the corresponding color channel; c) determining a total input colorant amount by combining the input colorant amounts for each color channel; d) for image pixels where the total input colorant amount exceeds the total colorant amount limit, determining depleted code values for each color channel such that the depleted code values produce substantially the input perceived color according to the device color model and wherein the total colorant amount corresponding to the depleted code values is less than or equal to the total colorant amount limit; and e) repeating steps (a) through (d) for a plurality of pixels in the input digital image.