Calibration of color cameras requires that a calibration pattern is recorded and color responsivity curves are estimated from the recorded data. Very often, these curves are sampled at discrete wave-length, so that the calibration problem can be written as a system of linear equations. The solution of the – usually overdetermined – problem is subject to a constrained optimization problem, as these curves need to have a certain shape. In this article we apply different methods to incorporate constraints into the estimation problem while still keeping the problem linear.