A new method is devised for extracting diatomic electronic transition strengths, as functions of internuclear distance R, from total radiative decay rates as a function of the vibrational level upsilon’ in the excited electronic state. The method involves least-squares inversion and utilizes an efficient and reliable sum rule for total radiative decay. When applied to the available data for the B-X transition in I-2, the method indicates that the transition strength peaks at 1.85 +/- 0.1 D-2 near R = 3.3 Angstrom. This result is in qualitative agreement with most prior studies, from which, however, the level of quantitative consistency must be rated as poor.