The authors have measured the output spectrum and the threshold current in 9.2 mu m wavelength GaAs/Al0.45Ga0.55As quantum-cascade lasers at 115 K as a function of hydrostatic pressure up to 7.3 kbars. By extrapolation back to ambient pressure, thermally activated escape of electrons from the upper lasing state up to delocalized states of the Gamma valley is shown to be an important contribution to the threshold current. On the other hand leakage into the X valley, although it has a very high density of states and is nearly degenerate with the Gamma band edge in the barrier, is insignificant at ambient pressure.