We show that small structures can be defined in high mobility two‐dimensional electron gases formed at a depth of 2770 A˚ below the surface in GaAs/Al0.33Ga0.67As heterostructures. The differential conductance of one‐dimensional constrictions defined by split gates in such deep electron gases showed more than 20 quantised plateaus. The absence of resonant structures on the plateaus demonstrates the absence of potential fluctuations in the constrictions. By applying a dc source‐drain bias we have measured the energy spacings of the first 18 subbands, and the effect of a small perpendicular magnetic field on the energy spacings has been investigated. ©1995 American Institute of Physics.