Cohesin entraps sister DNAs within tripartite rings created by pairwise interactions between Smc1, Smc3, and Scc1. Because the ATPase heads of Smc1 and Smc3 can interact with each other, cohesin rings in fact have the potential to form a variety of sub-compartments. Using in vivo cysteine crosslinking, we show that when Smc1 and Smc3 ATPases are engaged in the presence of ATP (E heads) cohesin rings generate a "SMC (S) compartment" between hinge and E heads and a "kleisin (K) compartment" between E heads and their associated kleisin subunit. Upon ATP hydrolysis, cohesin's heads associate with each other in a very different mode, in which their signature motifs and their coiled coils are closely juxtaposed (J heads), creating alternative S and K compartments. We show that all four sub-compartments exist in vivo, that acetylation of Smc3 during S phase is accompanied by an increase in the ratio of J to E heads, and that sister DNAs are entrapped in J-K but not E-K compartments or in either type of S compartment.