The structures and incremental binding enthalpies of cation-ligand complexes formed from a single coinage metal cation (Cu+, Ag+ and Au+) and as many as four dimethyl ether (DME) ligands are studied with second-order perturbation theory (MP2) and coupled cluster theory (CCSD(T)). Basis sets of up to augmented quintuple zeta quality were used in an effort to minimize basis set truncation error. The present results are compared with recent collision-induced dissociation measurements for the Cu+(DME)(n) complexes, as well as with related complexes in which water either replaces dimethyl ether as the ligand or alkali metal cations (Li+, Na+, and K+) replace the coinage metals. Agreement between the theoretical and experimental incremental binding enthalpies is good for the two larger copper complexes: DeltaH(0)(Cu+(DME)(3)) = 13.9 (theory) vs 13.1 +/- 0.9 kcal/mol (expt) and DeltaH(0)(Cu+(DME)(4)) = 11.5 (theory) vs 10.8 +/- 2.3 (expt), where values are expressed in kcal/mol. For the two smaller, more tightly bound copper complexes, the level of agreement is somewhat poorer: DeltaH(0)(Cu+(DME)) = 48.4 (theory) vs 44.3 +/- 2.7 kcal/mol (expt) and DeltaH(0)(Cu+(DME)(2)) = 50.6 (theory) vs 46.1 +/- 1.8 (expt). In general, DME binds copper, silver, and gold 15-25% more strongly than water binds the same cations.