We use the sky-average spectrum measured by EDGES High-band (90–190 MHz) to constrain parameters of early galaxies independent of the absorption feature at 78 MHz reported by Bowman et al. These parameters represent traditional models of cosmic dawn and the epoch of reionization produced with the 21cmFAST simulation code. The parameters considered are (1) the UV ionizing efficiency (ζ); (2) minimum halo virial temperature hosting efficient star-forming galaxies (); (3) integrated soft-band X-ray luminosity (); and (4) minimum X-ray energy escaping the first galaxies (E 0), corresponding to a typical H i column density for attenuation through the interstellar medium. The High-band spectrum disfavors high values of and ζ, which correspond to signals with late absorption troughs and sharp reionization transitions. It also disfavors intermediate values of , which produce relatively deep and narrow troughs within the band. Specifically, we rule out (95% C.L.). We then combine the EDGES High-band data with constraints on the electron-scattering optical depth from Planck and the hydrogen neutral fraction from high-z quasars. This produces a lower degeneracy between ζ and than that reported by Greig & Mesinger using the Planck and quasar constraints alone. Our main result in this combined analysis is the estimate (95% C.L.). We leave the evaluation of 21 cm models using simultaneously data from EDGES Low- and High-band for future work.