We have studied the effects of very narrow potential barriers on the transport through short one-dimensional GaAs-AlxGa1-xAs wires. The barrier is applied by a 45-nm-wide gate to a nominally 2-m-wide two-dimensional electron gas. The measurements reveal reproducible fluctuations in the transconductance whose origin is unknown. It might be that the fluctuations are associated with the slight disorder in the devices. The possibility that the fluctuations result from transmission resonances is also discussed. © 1988 The American Physical Society.