Accurate and homogeneous atmospheric parameters (Teff, logg, Vt, [Fe/H]) are derived for 74 FGK non-variable supergiants from high-resolution, high signal-to-noise ratio, echelle spectra. Extremely high precision for the inferred effective temperatures (10-40K) is achieved by using the line-depth ratio method. The new data are combined with atmospheric values for 164 classical Cepheids, observed at 675 different pulsation phases, taken from our previously published studies.