The instability of supersonic mixing layers, with velocity profiles possessing a wake component, is investigated using linear, inviscid, spatial theory. The mean-velocity profile is represented by a hyperbolic-tangent profile plus a wake component. Such profiles are encountered in the initial region of experimental supersonic shear-layer flows, as well as in envisaged hypersonic propulsion systems in which ingested boundary layers generate substantial wake components. Shear-layer and wake instability modes previously found in incompressible mixing layers are also found in compressible mixing layers. The existence of a wake component in the velocity profile renders the mixing layer more unstable at all free-stream Mach numbers. For convective Mach numbers exceeding unity, the shear-layer mode splits into two supersonic modes, and the mixing layer becoming more unstable with increasing wake deficit. The wake mode becomes less unstable and eventually stable with increasing compressibility, i.e., increasing convective Mach numbers.