High fidelity chromosome segregation during mitosis requires that cells identify the products of DNA replication during S-phase and then maintain that identity until anaphase onset. Sister chromatid identity is achieved through cohesin complexes (Smc1, Smc3, and Mcd1 and Irr1/Scc3), but the structure through which cohesins perform this task remains enigmatic. In the absence of unambiguous data, a popular model is that a subset of cohesin subunits form a huge ring-like structure that embraces both sister chromatids. This 'one-ring two-sister chromatid embrace' model makes clear predictions--including that premature cohesion loss in mitotic cells must occur through a substantial reduction in cohesin-DNA associations. We used chromatin immunoprecipitation to directly test for cohesin dissociation from well-established cohesin binding sites in mitotic cells inactivated for Pds5--a key cohesin regulatory protein. The results reveal little if any chromatin dissociation from cohesins, despite a regimen that produces both massive loss of sister chromatid tethering and cell inviability. We further excluded models that cohesion loss in mitotic cells inactivated for Pds5 arises through either cohesin subunit degradation, premature Hos1-dependent Smc3 de-acetylation or Rad61/WAPL-dependent regulation of cohesin dynamics. In combination, our findings support a model that cohesin complexes associate with each sister and that sister chromatid cohesion likely results from cohesin-cohesin interactions. We further assessed the role that Pds5 plays in cohesion establishment during S-phase. The results show that Pds5 inactivation can result in establishment defects despite normal cohesion loading and Smc3 acetylation, revealing a novel establishment role for Pds5 that is independent of these processes. The combination of findings provides important new insights that significantly impact current models of both cohesion establishment reactions and maintenance.