Experimental measurements on III-V semiconductor structures in which a delta-doped plane has been placed inside a quantum well have shown good in-plane carrier velocity characteristics at high carrier concentrations; such structures have applications in power field effect transistors. To investigate the physics underlying the transport in these layered structures, we have obtained the velocity-field characteristics for the channel electrons with an ensemble Monte Carlo simulation that takes into account the confinement of the electrons within the quantum well. Our results compare well with experiment, especially given that there are no adjustable parameters. We show that high-field channel velocities v sat are much more affected by K-space transfer between and L valleys than by real-space transfer into the barrier material. The velocity-field curves are sensitive to the position of the delta-doped plane, for example the low-field mobility is lowered as the delta-doped plane approaches the centre of the quantum well because the overlap of the lowest subband electron wavefunction with the delta-doped plane is greatest. We have also suggested an explanation for a correlation between low-field mobility and saturation velocity deduced from experimental data.