An inversion technique to recover LTE one-dimensional model photospheres for late-type stars, which was previously applied to the Sun by Allende Prieto et al. in 1998, is now employed to reconstruct, semiempirically, the photospheres of cooler dwarfs: the metal-poor Groombridge 1830 and the active star of solar metallicity ɛ Eridani. The model atmospheres we find reproduce satisfactorily all the considered weak-to-moderate neutral lines of metals, satisfying in detail the excitation equilibrium of iron, the wings of strong lines, and the slope of the optical continuum. The retrieved models show a slightly steeper temperature gradient than flux-constant model atmospheres in the layers where logτ<=-0.5. We argue that these differences should reflect missing ingredients in the flux-constant models and point to granular-like inhomogeneities as the best candidate. The iron ionization equilibrium is well satisfied by the model for Gmb 1830, but not for ɛ Eri, for which a discrepancy of 0.2 dex between the logarithmic iron abundance derived from neutral and singly ionized lines may signal departures from LTE. The chemical abundances of calcium, titanium, chromium, and iron derived with the empirical models from neutral lines do not differ much from previous analyses based on flux-constant atmospheric structures.