Recent advances in the resolution of observational data have required a much greater degree of accuracy in the determination of oscillator strengths than has been necessary in the past. We discuss how corresponding theoretical advances are leading to improved accuracy in the calculation of wave functions of atomic states, resulting in oscillator strengths whose uncertainties are within acceptable limits. We show the importance of using experimental energies in refiningab initiocalculations, and we illustrate these developments by considering difficult transitions in Mg II, Na III, and Fe II. ©2000 American Institute of Physics.