Details of the K x-ray emission spectra of K+ and Cl- in KCl are discussed. It is shown that the valence hole is effectively localized to one atomic site during the lifetimes of both the potassium and chloride 1s holes. This localization is found to be an appreciable factor in the processes contributing to the emission. Calculations of the relative intensity of the cross-transition lines, of the type 1sK-1-->3pC1-1, Kβ5, are reported. The results of the calculations agree, to within 40%, with the observed values. The widths of the valence emission lines, due to the transitions 1sK-1-->3pC1-1 and 1sC1-1-->3pC1-1, Kβ1, 3 are considered. Because of the localization of the final hole state, both initial and final hole states of the Kβ1, 3 transition see the same crystal potential, and thus there is no first-order broadening due to spatial variation of that potential. This is not the case for the cross-transition line Kβ5. A model due to Dexter is then used to show that the corrected width of the Kβ5 line should be about 0.5 eV greater than that for Kβ1, 3. This corresponds to the observations made by Deslattes.