Accurate neutron-diffraction measurements from crystals suffering from severe extinction have been used to test the recent general theory of extinction of Zachariasen (Acta Cryst. (1967). 23, 558). Analysis of these measurements indicates that certain of the approximations made in the theory are not generally valid and result in systematic deviations between theory and experiment, namely a marked angle-dependent effect and an inadequacy of the theory for strong extinction. The original theory is therefore extended to take these factors into account and to give agreement with the observed data.