The Gay-Berne potential is proving to be of considerable value in computer simulation studies of liquid crystals. However, the parameters employed in the potential were chosen by comparison with that for a line of four Lennard-Jones centres; they may not, therefore, be appropriate for mesogenic molecules. To see if this is the case we have estimated the parameters in the Gay-Berne potential by comparison with the site-site potential constructed forp-terphenyl, which has a molecular structure typical of many mesogens. Unlike the Gay-Berne potential the site-site potential is biaxial, and a method for projecting out this biaxiality is proposed. The resultant uniaxial model has then been used to obtain values for the parameters occurring in the Gay-Berne potential. These are found to differ significantly from those proposed originally; they are, we believe, more appropriate for investigations of the behaviour of liquid crystals. Our own molecular dynamics simulations, based on the new parametrization, reveals the existence of isotropic, nematic and smectic A phases. The results, in common with those from previous studies, indicate that the structure of the isotropic and nematic phases of the Gay-Berne mesogen are dominated by short range anisotropic repulsive forces. In marked contrast, the stability of the smectic A phase is found to be critically dependent upon the anisotropy in the attractive forces.