1. A method for reproducing an image, the method comprising: determining a change required in a selected base point in an input colorant space of a digital-image rendering system to obtain from the digital-image rendering system a desired reference output color to within a predetermined color tolerance, wherein the determination of the change is based on a local approximation of a colorant/color relationship at the selected base point; and reproducing the image on the rendering system by changing selected colorant combinations of the image based on the result of determining the change required in a selected base point, wherein the determination of the change based on a local approximation comprises: a) the selecting of a selected color attainable via the local approximation that is proximate to the color obtainable via the local approximation that is closest to the desired reference output color with respect to some measure of color difference; and b) the selecting of, out of all changes to the selected base point that lie within a unit colorant hypercube of digital-image colorant combinations and that produce the selected color, a change that is close to the change that is smallest out of all changes to the selected base point that lie within a unit colorant hypercube of digital-image colorant combinations and that produce the selected color with respect to some measure of magnitude.