The molecular structure of small CuxSy- anionic clusters, some of which are odd-electron species, was studied by combination of ab initio and atoms-in-molecules (AIM) calculations. It is found that covalent Cu-Cu bonding is weak, unstable and often is not realized, even though interatomic distances are found to be within the normal Cu-Cu bond range. Three new stable CuxSy- clusters are revealed. On the basis of the structure of the new isomers, the relationship between reactivity of CuxSy- ions with P-4 and coordination of sulfur atoms in the clusters is established.