Bandgaps and transitions

I don't really understand why materials with an indirect bandgap are not very optically active. I understand that in these materials to go from the top of the valence band to the bottom of the conduction band is unlikely due to the extra requirement of phonons, but surely you can still have a direct transition from the valence to conduction band at an energy higher than the bandgap energy?

(Despite studying this for a lot of last year, my understanding is somewhat limited so this is a bit of a guess.)

Certainly, there can be direct transitions from valence to conduction band for indirect band gap metals. If you look at a graph of absorption coefficient against photon energy for germanium, for instance, it looks like there are two band gaps - onsets of absorption at 0.73eV and another sharp increase at 0.87eV. The first value is the minimum energy difference between the two bands; the second is the minimum where no change in wavenumber is needed.

That would seem to imply that indirect band gap semiconductors are only not very optically active when looking at wavelengths between the two energies. Once photons are more energetic than the energy gap for direct transitions, I can't think of a reason why it wouldn't be optically active (although there might be one).