We have grown high mobility one-dimensional electron gases by molecular-beam epitaxy (MBE) on etched GaAs pnpnp facets. By applying the appropriate bias to the p- and n-GaAs layers which serve as a unique backgate, the electron gas width and mobility may be controlled. The width may be varied between about 400 and 100 nm. We also find that the mobility increases up to about 6 X 10(5) cm2/V s, rather than decreases with falling carrier concentration.