A new method for carrying out approximate mean-field calculations is presented. The method involves carrying out the calculations in a restricted basis built up from the single-particle states of the parametrized Ginocchio potential. Calculations are reported for doubly magic and semimagic nuclei, both normal and exotic. Good qualitative reproduction of the results of self-consistent mean-field calculations is achieved, especially for those properties that relate to the nuclear surface. The results suggest that the optimal Ginocchio eigenstates are good approximations of the canonical basis states of full Hartree-Fock-Bogolyubov approximation, both for bound states and for those at moderately low positive energies.