In this article we introduce a new method for estimating camera sensitivity functions from spectral power input and camera response data. We also show how the procedure can be extended to deal with camera nonlinearities. Linearization is an important part of camera characterization, and we argue that it is best to jointly fit the linearization and the sensor response functions. We compare our method with a number of others, both on synthetic data and for the characterization of a real camera. All data used in this study is available online at www.cs.sfu.ca/similar tocolour/data.