The lowest-energy isomers of Cu N clusters for N 20-30 are identified using an unbiased search algorithm and density functional theory calculations. The low-energy structures over this size range are dominated by those based on a 13-atom icosahedral (I h) core and a 19-atom double icosahedron (DI h) core. A transition in the ground-state isomers from I h-based to DI h-based structures is predicted overt N 21-23. We discuss this transition in the broader context of the growth pattern for Cu N over N 2-30 that features regions of gradual evolution in which atoms successively add to the cluster surface, separated by sudden changes to a different structural organization and more compact shape. These transitions result from a competition between interatomic bonding energy and surface energy. The implications of this growth pattern for the further evolution of copper from microstructure to bulk are discussed.