Wannier theory is critically reexamined and compared with semiclassical S-matrix theory, which serves as a reference calculation. We find that for certain situations classical half-collision calculations with a fixed reaction zone radius strongly differ from the results of a full S-matrix treatment even at energies very close to threshold. By giving a parameter-free description of an energy-dependent reaction zone radius we take the initial state more accurately into account in the half-collision approach. This extension produces results for ionization probabilities which are in excellent agreement with the full-collision semiclassical S-matrix theory. [S1050-2947(99)09011-3]