A laboratory model is used to investigate the effects of sloping boundaries on homogeneous wind-driven β-plane circulation. The very gentle slopes of real oceanic boundaries raise the possibility that dissipation by lateral diffusion of vorticity to the boundary is largely removed, leaving dissipation only in bottom Ekman layers. The laboratory model is a modification of the rotating ‘sliced-cylinder’ introduced by Pedlosky and Greenspan (1967) and Beardsley (1969) and in which flow is driven by a differentially rotating lid. The vertical wall is replaced with a side wall having a uniform 45° slope around the entire perimeter. This sloping boundary, like a continental slope, tends to steer the flow along the slope. In the geometry chosen for this study it also provides closed potential vorticity contours through every point in the basin, thus removing the blocked contours of the experiments with a vertical wall and the open contours of ocean basins that approach the equator. For cyclonic forcing there is a northward (Sverdrup) flow in the interior superimposed on a zonal flow so that a particle starts out at the southwest, enters the slope region in the northwest, circles cyclonically along a circle of constant radius (and depth) to a point on the southeast where it crosses constant depth contours and rejoins the original point. The direction of flow is reversed for anticyclonic forcing. The main dissipation of vorticity takes place in the southeast where the flow crosses constant depth contours. For cyclonic forcing the flow is stable and steady under all conditions achieved. For anticyclonic forcing the laboratory flow is unsteady under all conditions attainable and unstable to eddy shedding at sufficiently large Rossby or Reynolds numbers. At large Ekman numbers the onset of instability corresponds to shedding of cyclonic eddies in the region where the boundary current enters the interior, whereas at small Ekman numbers it corresponds to periodic breakup of an anticyclonic gyre in the ‘northwest’ and the formation of anticyclonic eddies. Eddies of both sign are shed when the forcing is sufficiently supercritical and the Ekman number small. A simple, qualitative argument explains why the cyclonic flow is stable and the anticyclonic flow is unstable when the system is nonlinear.