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A variationally stable, adiabatic hyperspherical treatment of two- and three-photon detachment of H- is presented. Results are compared with analytic predictions of a zero-range potential model of H-. Detailed comparisions are made also with other theoretical results which include the effects of electron correlations. We predict analytically (and demonstrate numerically) an extreme sensitivity of the theoretical predictions to any errors in the value of the electron affinity employed. In an Appendix we show that the low-intensity limit of the Keldysh treatment [Sov. Phys. JETP 20, 1307 (1965)] of detachment of an electron bound in a zero-range potential agrees with the results of a perturbative treatment.