The structure of self-organized quantum wires buried at the interfaces of a SiGe/Si multilayer is investigated by grazing incidence small-angle x-ray scattering. A nearly periodic distribution of wires, well described by a short-range ordering model, gives rise to intensity satellite maxima in reciprocal space. The shape of the wire cross section is determined from the heights of these intensity maxima, and the analysis reveals that the conventional step-bunching model is not sufficient to explain the wire shape.