Polaritons are formed when the electromagnetic field couples to excitons in a semiconductor. In their high-quality semiconductor quantum microcavities, Fisher et al. observe an unexpected decrease in the polariton linewidth (the full width at half maximum) near resonance. This paper uses Green's-function methods to show how the exciton linewidth and the cavity losses combine together, and that they can give a polariton linewidth reduced below that of either of its components. The quantum well disorder is described as a spatially varying potential due to both alloy fluctuations and well width variation, which causes the exciton component to become broadened. \textcopyright{} 1996 The American Physical Society.