Formal conditions are derived for the stability of a velocity discontinuity at a plane interface between two perfectly conducting, inviscid, compressible fluids, in the presence of uniform magnetic fields. Certain special cases, in which the stability conditions can be simplified, are discussed in detail. Previous results for incompressible fluids are rederived and it is shown that the introduction of a slight compressibility always reduces the stabilizing effect of magnetic fields. It is further shown that in two special cases the magnetic field required to stabilize an interface continues to increase with the introduction of more compressibility until it reaches a limiting value that is about twice as large as the value appropriate to incompressible fluids.