Abstract The general problem of reducing a frequency-dependent radiative transfer problem to an equivalent grey problem is discussed. In particular, we construct, from the integral transport equation, an asymptotic solution to be used in forming grey opacities. We also show how the angular dependence of this asymptotic result can be incorporated into the grey equation without introducing an angularly dependent opacity. One needs only to modify the scattering kernel. Our resulting grey equation is shown to be exact in the two limiting cases of optically thin and thick systems, where it is well known that the Planck and Rosseland means, respectively, are the appropriate averages. As an example of these considerations, we apply our results to the Elsasser band and calculate generalizations, to non-zero temperature gradients, of the Planck and Rosseland means.