We report the results of deep level transient spectroscopy experiments with the second ionization level of the double donor defect (EL2) under uniaxial stress in p-type GaAs. We measure the shift in the hole emission rate as a function of stress applied in the [100] and [110] directions. By modeling the valence band with two independently displacing bands and appropriately derived effective masses, we determine the absolute hydrostatic pressure derivative of the defect to be 39±15 meV GPa−1. The shear contribution is negligible. These results are very different from those obtained for the first ionization level, which has a much higher absolute pressure derivative of 90 meV GPa−1.