A suggestion to improve upper limits on the existence of dipole moments in atoms is discussed. Parity and time reversal violating components in the nuclear force may produce P, T-odd moments in nuclei which, in turn, induce such moments in atoms. In order to improve the sensitivity, one must use atoms with a high Z. Atoms with nuclei that have both quadrupole and octupole deformations in the ground state have enhanced Schiff moments when there are forces that violate the time reversal and reflection symmetries. These Schiff moments produce enhanced dipole moments in the atom.