We present non-LTE corrections to abundances of Fe, O, Na, and Mg derived from LTE analyses of F-K stars over a broad range of gravities and metal abundances; they were obtained using statistical equilibrium calculations and new model atoms. Line opacity was considered by means of an empirical procedure where it was attributed to a veil of weak Fe I lines; in the case of solar-type dwarfs, results were compared with those obtained using (LTE) mean intensities computed from OSMARCS models. We think that the empirical procedure produces better results for metal-poor stars, while mean intensities should perhaps be preferred for the Sun (where departures from LTE are anyway not very large). Collisions with both electrons and H I atoms were considered. Since cross sections for this second mechanism are very poorly known, we calibrated them empirically by matching observations of RR Lyrae variables at minimum light (discussed in Clementini et al., 1995, Cat. <J/AJ/110/2319>). These stars were selected because non-LTE effects are expected to be larger in these stars than in those usually considered in the study of the chemical evolution of the Galaxy (cool main sequence and red giant branch stars). We found that different non-LTE mechanisms are important for the different species and transitions considered; on the whole, our calculations yielded moderate corrections to LTE abundances for high excitation O lines in warm dwarfs and giants, Na and Mg lines in giants and supergiants, and Fe I lines in F-supergiants (where corrections becomes very large for IR O lines). Non-LTE corrections were found to be negligible in the other cases studied.