ABSTRACT Condensin is a Structural Maintenance of Chromosomes (SMC) complex needed for the compaction of DNA into chromatids during mitosis. Lengthwise DNA compaction by condensin is facilitated by ATPase-driven loop extrusion, a process that is believed to be the fundamental activity of most, if not all SMC complexes. In order to obtain molecular insights, we obtained cryo-EM structures of yeast condensin in the presence of a slowly-hydrolysable ATP analogue and linear, as well as circular DNAs. The DNAs were shown to be “clamped” between the engaged heterodimeric SMC ATPase heads and the Ycs4 subunit, in a manner similar to previously reported DNA-bound SMC complex structures. Ycgl, the other non-SMC subunit was only flexibly bound to the complex, while also binding DNA tightly, and often remaining at a distance from the head module. In the clamped state, the DNA is encircled, or topologically entrapped, by the kleisin Brnl and the two engaged head domains of Smc2 and Smc4, and this tripartite ring is closed at all interfaces, including at the neck of Smc2. We show that the neck gate opens upon head engagement in the absence of DNA, but it remains shut when DNA is present. Our work demonstrates that condensin and other SMC complexes go through similar conformations of the head modules during their ATPase cycle. In contrast, the behaviour of the Ycgl subunit in the condensin complex might indicate differences in the implementation of the extrusion reactions and our findings will constrain further mechanistic models of loop extrusion by SMC complexes. SIGNIFICANCE STATEMENT DNA needs to be compacted dramatically to fit into nuclei and during cell division, when dense chromatids are formed for their mechanical segregation, a process that depends on the protein complex condensin. It forms and enlarges loops in DNA through loop extrusion. Our work resolves the atomic structure of a DNA-bound state of condensin in which ATP has not been hydrolysed. The DNA is clamped within a compartment that has been reported previously in other SMC complexes, including Rad50, cohesin and MukBEF. With the caveat of important differences that we also uncovered, it means that all SMC complexes cycle through at least some similar states and undergo similar conformational changes in their head modules, while hydrolysing ATP and translocating DNA.