Two approximations for the inclusion of scalar relativistic effects into otherwise nonrelativistic molecular self-consistent field calculations are described, which continue the sequence of approximations from previous work. In the first, the two-electron contributions are confined to those where each small component density is one-center. In the second, the two-electron contributions are approximated by using the bare Coulomb operator, an approach which parallels the Douglas-Kroll-Hess method. The results show that both approximations yield results close to the full two-electron scalar relativistic method, within 0.001 Angstrom in bond lengths and 0.1 kcal/mol in dissociation energies. The approximations also give results which are very similar to those of the Douglas-Kroll-Hess method. The second approximation is similar in cost to the Douglas-Kroll-Hess method and only contains simple operators whose integrals are easy to evaluate.