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The conditions necessary for partially coherent scattering to influence the thermalization depth are investigated, and the effects of partial redistribution in homogeneous slab atmospheres are approximated using several common resonance lines as examples. For electron densities above 10 exp 10/cu cm, it is concluded that even when coherent scattering dominates the escape process, the thermalization depths of the strongest resonance lines of H, Ca II, and Mg II agree roughly with the Doppler diffusion in frequency. No elastic scattering effects on the thermalization of Mg II h and k and Ca II H and K are found. At lower densities, such as for giant star chromospheres and QSO models, the results deviate strongly from the Doppler complete redistribution case.