Most conventional methods of determining the dipole moment &mgr; are unsatisfactory when applied to transitions between degenerate levels; this is because the overlapping of transitions among magnetic sub‐levels modifies the photo‐excitation behavior in a complex way. To overcome this difficulty, two novel methods of determination are presented. One makes use of differently polarized laser light, and yields a set of excitation curves specific to each polarization. By treating &mgr; as a parameter and fitting the curves through calculations, one can obtain the value of &mgr;. In the other method, a magnetic field is applied to the atom under study in order to raise its degeneracy. As a result, simple Rabi oscillations manifest themselves and one can derive &mgr; directly from their frequencies. These two methods of determining &mgr; are tested on absorption lines in uranium, demonstrating that they work quite well and improve the accuracy of measured dipole moments. ©1996 American Institute of Physics.