The theory of optical photon echo and hole burning spectroscopies in low temperature glasses is discussed within the framework of the tunneling two-level system and stochastic sudden jump models. Exact results for the relevant theoretical quantities involve certain averages over the distributions of the two-level system energies and relaxation rates. The standard approximations for these averages are critically examined, for experimentally realistic parameters, via comparison to numerically exact calculations. The general conclusion is that the standard approximations are often used under conditions where they are not expected to be quantitatively accurate. (C) 1997 American Institute of Physics.