The presence of ice shelf basal channels has been noted in a number of Antarctic and Greenland ice shelves, but their impact on basal melting is not fully understood. Here we use the Massachusetts Institute of Technology general circulation model to investigate the effect of ice-shelf basal channels on oceanic melt rate for an idealised ice shelf resembling the floating tongue of Petermann Glacier in Greenland. The introduction of basal channels prevents the formation of a single geostrophically balanced boundary current; instead the flow is diverted up the right-hand (Coriolis-favoured) side of each channel, with a return flow in the opposite direction on the lefthand side. As the prescribed number of basal channels is increased the mean basal melt rate decreases, in agreement with previous studies. For a small number of relatively wide channels the sub-ice flow is found to be a largely geostrophic horizontal circulation. The reduction in melt rate is then caused by an increase in the relative contribution of weakly-melting channel crests and keels. For a larger number of relatively narrow channels, the sub-ice flow changes to a vertical overturning circulation. This change in circulation results in a weaker sensitivity of melt rates to channel size. The transition between the two regimes is governed by the Rossby radius of deformation. Our results explain why basal channels play an important role in regulating basal melting, increasing the stability of ice shelves.