In this work, the ground states of CdiOi clusters (i = 1-9, 12, 15) are studied. Ringlike structures have been found to be the global minima for clusters as large as i = 7, and three-dimensional structures (clustertubes and spheroids) are observed to be the global minima for larger ones (i = 8, 9, 12, 15). This trend has been ascribed to the stability of obtuse O-Cd-O angles in the first case, and to the stability gained from higher coordination in the second case. The three-dimensional structures may be envisioned as being built from Cd2O2 and Cd3O3 rings, as it is the case for ZniXi (where X = O, S, Se, Te) three-dimensional structures. Calculated cohesive energies increase as the cluster size increases, which gives support to the idea that the predicted global minima are the correct ones.