In ionization chamber dosimetry close to brachytherapy sources, the non-uniform photon fluence in the vicinity of the air cavity of the ionization chamber must be corrected for. In this paper, experimentally determined relative non-uniformity correction factors are determined for a PTW23331 chamber and a number of Farmer-type chambers. It is concluded that the `anisotropic' theory of Bielajew agrees better with the experimental results than the `isotropic' theory of Kondo and Randolph. The experiments show that neither the material choice nor the radius of the central electrode have any significant effect on the non-uniformity correction factors. Experiments on the wall-material dependence in the non-uniformity correction factor, which is predicted by the anisotropic theory, were inconclusive. Parameters for the Farmer-type chambers for calculation of theoretical non-uniformity correction factors are given. Data to derive anisotropic fluence non-uniformity correction factors are given in tabular form. An error in the Kondo and Randolph equations is reported and the corrected equations presented.