Reaction of [Cp*Ir(P-P)Cl][B(C6F5)(4)] (P-P = bisdimethydiphosphinomethane (dmpm), bisdiphenyldiphosphinomethane (dppm)) with [Et3Si][B(C6F5)(4)] in methylene chloride under 1 atm of hydrogen gas affords the dicationic compressed dihydride complexes [Cp*Ir(P-P)H-2][B(C6F5)(4)](2). These dicationic complexes are highly acidic and are very readily deprotonated to the corresponding monohydride cations. When the preparative reaction is carried out under HD gas, the hydride resonance exhibits J(HD) = 7-9 Hz, depending upon the temperature of observation, with higher values of J(HD) observed at higher temperatures. A thermally labile rhodium analogue, [Cp*Rh(dmpm)(H-2)][B(C6F5)(4)](2), was prepared similarly. A sample prepared with HD gas gave J(HD) = 31 Hz and J(HRh) = 31 Hz, allowing the Rh complex to be identified as a dihydrogen complex. Quantum dynamics calculations on a density functional theory (DFT) potential energy surface have been used to explore the structure of the Ir complexes, with particular emphasis on the nature of the potential energy surface governing the interaction between the two hydride ligands and the Ir center.