Internal conversion (IC) between excited electronic states is a fundamental photophysical process that is important for understanding protection from UV radiation, energy transfer pathways and electron injection in artificial photosynthetic systems and organic solar cells. We have studied IC between three singlet MLCT states in an iridium complex using femtosecond fluorescence spectroscopy. Very fast IC with a time constant of <20 fs is observed from the highest state and a much slower relaxation to the lowest energy singlet state on a 70 fs time scale. The abrupt slowdown of the relaxation rate occurs when there is >0.6 eV of vibrational energy stored in the complex that has to be dissipated by intramolecular vibrational redistribution before further IC to the lower energy states can occur. These results show that the ability to dissipate vibrational energy can control the relaxation process in this class of materials.