The structure and composition of the three low index surfaces (100), (110) and (111) of the substitutionally disordered alloy Mo0.75Re0.25 was investigated by full dynamical LEED intensity analyses. Strong face-dependencies are found for the composition of the surface layers as well as for the relaxation of their spacings. The ( 110) orientation turns out to be almost bulk-like terminated geometrically as expected for a quasi-close packed surface as well as chemically. The more open (100) and (111) surfaces, however, exhibit heavily oscillating layer stoichiometries and strong relaxations of interlayer distances both extending deep below the surface. The face-dependent segregation behaviour can be consistently explained by a surface induced tendency to stabilize an ordered intermetallic compound with the order parameter rapidly decaying with depth.