A modification of the Orbach relaxation process arising from the phonon-induced intermediate level width is developed. It is shown from a numerical integration, including all two-phonon terms (resonant, interference, nonresonant), that the temperature dependence of the two-phonon spin-lattice relaxation process at temperatures intermediate between the Orbach and Raman regimes can be substantially altered. Thus, determination of excited-state splittings using the temperature dependence of the Orbach relaxation rate can be misleading, should experimental considerations limit the range over which T measurements are made. In general, the effect of the intermediate level width is to diminish the slope of 1T1 vs 1T, yielding an apparent reduction in the excited splitting as compared to optical determinations. An apparent concentration dependence of the exponent in the Orbach relaxation process can also obtain from the same source, by virtue of a change in the sound velocity changing the intermediate level width.