ABSTRACT We present the evolution of the 21-cm signal from cosmic dawn and the epoch of reionization in an upgraded model including three subtle effects of Ly α radiation: Ly α heating, CMB heating (mediated by Ly α photons), and multiple scattering of Ly α photons. Taking these effects into account, we explore a wide range of astrophysical models and quantify the impact of these processes on the global 21-cm signal and its power spectrum. We find that Ly α heating raises the gas temperature by up to $\mathcal {O}(100)$ degrees (CMB heating adds a few more degrees) in models with weak X-ray heating, thus suppressing the predicted 21-cm signals. Varying the astrophysical parameters broadly in an attempt to cover the full plausible range of models, we find that in the upgraded model the absorption trough of the global signal reaches a lowest possible floor of −165 mK at redshifts z ≈ 15−19. This is in contrast with the predictions for a pure adiabatically cooling Universe, for which the deepest possible absorption is a monotonically decreasing function of cosmic time and is −178 mK at z = 19 and −216 mK at z = 15, dropping to even lower values at lower redshifts. With Ly α and CMB heating included we also observe a strong suppression in the low-redshift power spectra, with the maximum possible power (evaluated over the ensemble of models) attenuated by a factor of 6.6 at z = 9 and K = 0.1 Mpc−1. Finally, we find that at high redshifts corresponding to cosmic dawn, the multiple scattering of Ly α photons leads to an amplification of the power spectrum by a factor of ∼2−3 in all models.