We have carried out computational density functional investigations of Co I Re J (J=0,1,2; I+J=14) metal atom clusters. Through thorough optimization of geometry, spin polarization, and electronic configuration, the most stable structures for each cluster have been identified. While the global minima are found to be well defined and energetically well separated from other local minima, the study reveals a plethora of different structures and symmetries only moderately higher in energy. A key point of interest is the effect of doping the cobalt clusters with rhenium. Aside from significant structural reorganizations, rhenium is found to stabilize the clusters and couple down the spin. Furthermore, the most stable clusters comprise highly coordinated rhenium and, in the case of Co 12 Re 2, Re-Re bonding. Our results are compared to earlier experimental and computational data.