Spectroscopic studies have been carried out for GaAs crystals under hydrostatic pressure, intended for the investigation of effective-mass donor levels associated with different conduction-band minima and the DX center. Our results reveal the existence of three donor states appearing in the band gap. These are labeled ${\mathit{D}}_{\mathrm{\ensuremath{\Gamma}}}$, ${\mathit{D}}^{\mathrm{*}}$, and ${\mathit{D}}_{\mathit{X}}$. The donor state ${\mathit{D}}_{\mathrm{\ensuremath{\Gamma}}}$, normally observed at atmospheric pressure, successively crosses two other donor states (${\mathit{D}}^{\mathrm{*}}$ and ${\mathit{D}}_{\mathit{X}}$) as the hydrostatic pressure exceeds 28 kbar. ${\mathit{D}}^{\mathrm{*}}$, in turn, crosses ${\mathit{D}}_{\mathit{X}}$ at pressures of about 44 kbar. From their corresponding donor-acceptor pair luminescence, we know that ${\mathit{D}}_{\mathrm{\ensuremath{\Gamma}}}$ and ${\mathit{D}}_{\mathit{X}}$ have pressure dependences that track the \ensuremath{\Gamma}- and X-band minimum, and are believed to be effective-mass donor states associated with the \ensuremath{\Gamma}- and X-band edges, respectively. The third donor state ${\mathit{D}}^{\mathrm{*}}$ has a pressure dependence that does not seem to agree with any known conduction-band minimum. However, it is in many respects similar to the DX center, although it has not, in studies of radiative emission, revealed evidence of a large lattice relaxation and photoquenching effects.