The structure, binding energy, and hyperfine coupling constants of mononuclear copper carbonyls (Cu(CO)(n), n = 1-3) have been studied using extended basis sets with a number of different density functionals. In the case of CuCO, all the methods agree in forecasting a bent equilibrium structure with a significant barrier to linearity (approximate to 15 kJ mol(-1)). Hyperfine coupling constants computed for bent and linear structures are very similar, thus ruling out the need for a linear structure to explain the electron paramagnetic resonance spectrum. In agreement with experimental data, addition of a second CO molecule leads to a (2) Pi linear complex with vanishingly small hyperfine splittings but enhanced stability due to the reduction of two-orbital three-electron repulsive interactions. The bond pattern then remains essentially the same in Cu(CO)(3), which assumes a planar trigonal equilibrium structure. From a quantitative point of view, local density functionals give extremely high binding energies and also generalized gradient corrections are not sufficient to completely rectify matters. Introduction of some Hartree-Fock exchange in the functional delivers a further significant improvement, approaching the accuracy of the most refined post Hartree-Fock computations. Purposely tailored basis sets are also introduced which are small enough to be used in molecular computations but are essentially free from basis set superposition error.