We argue that the photon spectra in radiative decays of various heavy quarkonium states provide important information on their nature. If two of these states are in the strong coupling regime, we are able to produce a parameter-free model-independent formula, which holds at next-to-leading order and includes both direct and fragmentation contributions. When the formula is checked against recent CLEO data it favors Υ ( 2 S ) and Υ ( 3 S ) in the strong coupling regime and disfavors Υ ( 1 S ) in it.