Motivated by the geological sequestration of carbon dioxide (CO2), we study the propagation of gravity currents in a porous medium bounded by a thin layer of much lower permeability. We formulate a model for drainage assuming that the fluid remains simply connected throughout. Using this model we examine the propagation of both two-dimensional and axisymmetric currents numerically. We find that for the fixed-flux situation solutions approach a steady state which is described analytically. The approach to this final solution depends on both the permeability contrast and thickness of the thin layer, and in many cases the current first overshoots before relaxing back to its ultimate steady state. Finally, we examine propagation along multiple thin, lower permeability layers as a reduced-order model of the plume of CO2 currently being injected at Sleipner in the North Sea.