This paper describes a method for developing a transform between two device CMYK spaces in a way that preserves information about the black separation. An important application of such a transform exists in desktop color printers for proofing of electronic files prepared for offset printing.Our method uses a novel printer inversion approach based on constrained optimization. An error function defines the gamut mapping method and black separation behavior. The constraints limit the feasible solution region to the device gamut and prevent exceeding the maximum total area coverage. Colorant values corresponding to in-gamut colors are found with precision limited only by the accuracy of the device model. Out-of-gamut colors are mapped to colors within the boundary of the device gamut. An important property of our method is that areas in the input image using only black ink will be reproduced with the maximum possible black amount for a requested color.We present an application of this method to the creation of multidimensional lookup tables that can be packaged as ICC device link profiles.