Many authors have studied channeling radiation theoretically by means of the so called many beam approach. For axial channeling this approach tends to involve rather large eigenvalue problems if high accuracy is desired. With the extension to three-dimensional problems in mind we have therefore investigated the possibilities for a more efficient solution of these eigenvalue problems. The Lanczos algorithm [2] used in the preparation of Fig. 1 provides a substantial reduction of the numerical effort. We have also obtained some preliminary results for three-dimensional corrections to the tranverse problem. These corrections were found to be three-dimensional rather than longitudinal in character and tend to reduce the photon energy. The corrections are smaller than 1 percent for 4 MeV electrons in silicon. A more thorough investigation of these effects for the low energy part of the spectrum and a study of their impact on the high energy radiation [3] is now in progress. The conventional transverse many beam approach based on the Lindhard continuum approximation does not describe the latter effect.