We examine photodetachment of H- in parallel electric and magnetic fields, hv+H--->H+e- using semiclassical approximations. The fields cause the electron to return to the atom, producing recurrences that are visible as interference oscillations in the photodetachment cross section. As the energy is varied, new returning orbits are created through bifurcations. Each such new recurrence increases the complexity of the absorption spectrum, and each bifurcation causes a local failure of the semiclassical approximation. The failure is repaired by a Fresnel diffraction integral.