A stent-graft including a stent member having an inner surface and an outer surface, a generally tubular graft member and a coupling member that couples the stent member to the graft member. The coupling member, which is the preferred embodiment is in the form of a ribbon, covers only a portion of the inner or outer surface of the stent member and secures the stent member and graft member to one another. Alternatively, the coupling member can be described as interconnecting less than entirely the inner or outer surface of the graft member to the stent member. With this construction, regions of the stent member do not interfere with the coupling member. Shear stresses between the stent member and the coupling member and the risk of tearing the graft or coupling member or delamination therebetween may be reduced as compared to a fully enveloped stent member. This construction also provides improved flexibility and kink resistance.