The rotational damping width &Ggr;rot and the compound damping width &Ggr;comp are two fundamental quantities that characterize rapidly rotating compound nuclei having finite thermal excitation energy. A two‐component structure in the strength function of consecutive E2 transitions reflects the two widths, and it causes characteristic features in the double and triple gamma‐ray spectra. We discuss a new method to extract experimentally values of &Ggr;rot and &Ggr;comp. The first preliminary result of this method is presented. © 2003 American Institute of Physics