Anisotropic line-shape broadening (peak width which is not a smooth function of d-spacing) is frequently observed in powder diffraction patterns, and can be a source of considerable difficulty for whole-pattern fitting or Rietveld analysis. A model of the multi-dimensional distribution of lattice metrics within a powder sample is developed, leading naturally to a few parameters which can be varied to achieve optimal line-shape fits. Conditions on these parameters are derived for all crystal systems, and the method is illustrated with two examples: sodium p-hydroxybenzoate and rubidium fulleride.