A method is used for constructing a look up table for characterizing a printing device, and a system therefore, wherein the look up table is an inverse look up table for obtaining for the printing device colorant values in a colorant space as a function of given color values in a color space. The method includes: (a) selecting an axis in the color space; (b) selecting a path in the color space; (c) determining a particular point on the path having a predetermined colorant value; (d) projecting the particular point on the axis, thus obtaining a projected point; and (e) adding the projected point to the look up table as a sampling point.