The original three-body term in the Skyrme interaction is replaced by a two-body explicit density dependent term to reproduce simultaneously the excited and ground states of nuclei. Care has been taken to remove the spin instability of the Hartree-Fock ground state in nuclear matter and also the antipairing nature of the interaction inherent in the original Skyrme interaction. The spin-isospin dependent parameter introduced in the density dependent term is determined from the average asymmetry ratio and asymmetry energy. The modified Skyrme force is used to calculate the low-lying states of /sup 18/O, /sup 18/F, /sup 42/Ca, /sup 42/Sc, and /sup 16/O, /sup 40/Ca. In the light of these calculations the relative importance of the different Skyrme variants is studied.