It is known that, based on Wigner's rational approximation, the escape probability function can be improved by the insertion of geometry dependent constants. Bonalumi improved this method by replacing these constants by a function. The formulas derived here, based on general considerations, justify the form given by Bonalumi and generalize it to spheres as well. The results for a cylinder and a sphere are compared to the exact tabulated values, and show an error of <0.3% through the whole spectral region. Only one parameter is needed here. The method is shown to be insensitive to this parameter to a certain extent. Comparison is also made with the results achieved by the P0 + AP2 method. The treatment here is limited to an isolated lump, for cylinders and spheres only.