Tunneling-current measurements in Ga1-xAlxAs-GaAs-Ga1-xAlxAs heterostructures under hydrostatic pressure show that nonresonant tunneling occurs preferentially through the lowest potential barrier, while resonant tunneling is determined solely by a point profile. For fixed voltages, the low-temperature current through a 100 -40 -100 structure with Ga0.60Al0.40As barriers increased with pressure, up to 11 kbar. The rate of increase showed an abrupt rise at 4 kbar, which is attributed to tunneling through a -X barrier. This interpretation is consistent with a rapid increase of the tunneling current in AlAs-GaAs-AlAs, even at low pressures. On the other hand, a negative-resistance feature associated with resonant tunneling via quantum-well states, shifted smoothly to lower voltages with pressure, indicating that the energy of the confined states is established by a pressure-dependent -point profile. © 1986 The American Physical Society.