X-ray diffraction line profiles from the filings of cold-worked hexagonalclose-packed silver-antimony alloys have been recorded using a Geiger counter x-ray diffractometer and examined by Fourier analysis of line shapes. The composite broadening has been separated into that caused by particle size, lattice strain and the presence of stacking faults. The stacking-fault density has been found to be greatest for the alloy composition which is nearest to the primary face-centred-cubic phase boundary and to decrease almost linearly with increase in the solute content. The behaviour has been interpreted qualitatively in terms of the difference in free energies between the face-centred-cubic and hexagonal phases.