  Most work on foreground removal has treated the case where the frequency
dependence of all components is perfectly known and independent of position. In
contrast, real-world foregrounds are generally not perfectly correlated between
frequencies, with the spectral index varying slightly with position and (in the
case of some radio sources) with time. A method incorporating this complication
in presented, and illustrated with an application to the upcoming satellite
missions MAP and Planck. We find that even spectral index variations as small
as 0.1 can have a substantial impact on how channels should be combined and on
attainable accuracy.
