In this paper we introduce a new method for determining the relationship between signal spectra and camera RGB which is required for many applications in color. We work with the standard camera model, which assumes that the response is linear. We also provide an example of how the fitting procedure can be augmented to include fitting for a previously estimated non-linearity. The basic idea of our method is to minimize squared error subject to linear constraints, which enforce positivity and range of the result. It is also possible to constrain the smoothness, but we have found that it is better to add a regularization expression to the objective function to promote smoothness. With this method, smoothness and error can be traded against each other without being restricted by arbitrary bounds. The method is easily implemented as it is an example of a quadratic programming problem, for which there are many software solutions available. In this paper we provide the results using this method and others to calibrate a Sony DXC-930 CCD color video camera. We find that the method gives low error, while delivering sensors which are smooth and physically realizable. Thus we find the method superior to methods which ignore any of these considerations.