We apply various approaches describing the enhancement factor for the annihilation rate. The electron and positron band structures were obtained using the LMTO method. The calculated positron lifetimes are very sensitive to the description of the enhancement factor and for that reason it is a crucial test for the theory. Calculations were first tested on simple materials and then applied to the more complicated high-Tc copper oxides. We also present calculations of the momentum densities where the enhancement effect is less dramatic.