Level densities and spin cut-off factors have been investigated within the microscopic approach based on the BCS Hamiltonian. In particular, the spin cut-off parameters have been calculated at neutron binding energies over a large range of nuclear mass using the BCS theory. The spin cut-off parameters sigma(2)(E) have also been obtained from the Gilbert and Cameron expression and from rigid body calculations. The results were compared with their corresponding macroscopic values. It was found that the values of sigma(2)(E) did not increase smoothly with A as expected based on macroscopic theory. Instead, the values of sigma(2)(E) show structure reflecting the angular momentum of the shell model orbitals near the Fermi energy.