Most conventional methods of determining the dipole moment μ 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 μ as a parameter and fitting the curves through calculations, one can obtain the value of μ. 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 μ directly from their frequencies. These two methods of determining μ are tested on absorption lines in uranium, demonstrating that they work quite well and improve the accuracy of measured dipole moments.