Molecular cluster ions, which are stored in an electromagnetic trap under ultra-high vacuum conditions, undergo blackbody infrared radiative dissociation (BIRD). This process can be simulated with master equation modeling (MEM), predicting temperature-dependent dissociation rate constants, which are very sensitive to the dissociation energy. We have recently introduced a multiple-well approach for master equation modeling, where several low-lying isomers are taken into account. Here, we experimentally measure the BIRD of CO4●-(H2O)1,2 and model the results with a slightly modified multiple-well MEM. In the experiment, we exclusively observe loss of water from CO4●-(H2O), while the BIRD of CO4●-(H2O)2 leads predominantly to loss of carbon dioxide, with water loss occurring to a lesser extent. The MEM of two competing reactions requires empirical scaling factors for infrared intensities and the sum of states of the loose transition states employed in the calculation of unimolecular rate constants so that the simulated branching ratio matches the experiment. The experimentally derived binding energies are ΔH0(CO4●--H2O) = 45 ± 3kJ/mol, ΔH0(CO4●-(H2O)-H2O) = 41 ± 3kJ/mol, and ΔH0(CO2-O2●-(H2O)2) = 37 ± 3kJ/mol. Quantum chemical calculations on the CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVDZ level, corrected for the basis set superposition error, yield binding energies that are 2-5kJ/mol higher than experiment, within error limits of both experiment and theory. The relative activation energies for the two competing loss channels are as well fully consistent with theory.