The influence of relativistic, relaxation, and correlation effects on the low-lying energy levels of the 3d10, 3d94s, and 3d94p configurations of Cu II have been investigated. Large-scale multiconfiguration Dirac-Fock wave functions were applied to calculate the excitation energies and the electric-dipole-allowed transition probabilities and to allow for a systematic improvement of the computations. From these calculations, the theoretical lifetimes of the 3d94p levels are derived and compared with previous experiments and computations. Our results show that we provide not only an improved data basis for the low-lying levels of Cu II but also a useful computational model for studying other ions along the nickel isoelectronic sequence.