Buoyancy-driven surface currents were generated in the laboratory by releasing buoyant fluid from a source adjacent to a vertical boundary in a rotating container. Different bottom topographies that simulate both a continental slope and a continental ridge were introduced in the container. The topography modified the flow in comparison with the at bottom case where the current grew in width and depth until it became unstable once to non-axisymmetric disturbances. However, when topography was introduced a second instability of the buoyancy-driven current was observed. The most important parameter describing the flow is the ratio of continental shelf width W to the width L* of the current at the onset of the instability. The values of L* for the first instability, and L*−W for the second instability were not influenced by the topography and were 2–6 times the Rossby radius. Thus, the parameter describing the flow can be expressed as the ratio of the width of the continental shelf to the Rossby radius. When this ratio is larger than 2–6 the second instability was observed on the current front. A continental ridge allowed the disturbance to grow to larger amplitude with formation of eddies and fronts, while a gentle continental slope reduced the growth rate and amplitude of the most unstable mode, when compared to the continental ridge topography. When present, eddies did not separate from the main current, and remained near the shelf break. On the other hand, for the largest values of the Rossby radius the first instability was suppressed and the flow was observed to remain stable. A small but significant variation was found in the wavelength of the first instability, which was smaller for a current over topography than over a flat bottom.