It is shown that a coastal density current in a rotating system is unstable to downstream wave disturbances when the mean potential vorticity increases towards the (vertically-walled) coast and when the mean current vanishes there. Other new instability modes are also found which do not require the potential vorticity extremum of quasi-geostrophic theory. All the instabilities in our equivalent one-layer model release mean kinetic energy and most of them release mean potential energy, but an increase of the latter can occur under certain circumstances.