The White-Point Preserving Least Squares (WPPLS) algorithm is a method for colour correction that constrains the white point to be exactly mapped into its correct XYZ equivalent. For printers, however, the mapping is from device coordinates to colorimetric densities: the devicewhite is thus mapped into a zero vector and the WPPLS method cannot go forward. Here we use a polynomial regression model and specify that both white (the zero vector) and an average grey be exactly mapped. Moreover we extend the method to accurately but approximately map a subspace of the entire achromatic curve, thus reproducing the neutral tones with far greater accuracy.