In addition to inter-chromatid cohesion, mitotic and meiotic chromatids must have three physical properties: compaction into 'threads' roughly co-linear with their DNA sequence, intra-chromatid cohesion determining their rigidity, and a mechanism to promote sister chromatid disentanglement. A fundamental issue in chromosome biology is whether a single molecular process accounts for all three features. There is universal agreement that a pair of Smc-kleisin complexes called condensin I and II facilitate sister chromatid disentanglement, but whether they also confer thread formation or longitudinal rigidity is either controversial or has never been directly addressed respectively. We show here that condensin II (beta-kleisin) has an essential role in all three processes during meiosis I in mouse oocytes and that its function overlaps with that of condensin I (gamma-kleisin), which is otherwise redundant. Pre-assembled meiotic bivalents unravel when condensin is inactivated by TEV cleavage, proving that it actually holds chromatin fibres together.