Smc2/4 forms the core of the Saccharomyces cerevisiae condensin, which promotes metaphase chromosome compaction. To understand how condensin manipulates DNA, we used two in vitro assays to study the role of SMC (structural maintenance of chromosome) proteins and ATP in reconfiguring the path of DNA. The first assay evaluated the topology of knots formed in the presence of topoisomerase II. Unexpectedly, both wild-type Smc2/4 and an ATPase mutant promoted (+) chiral knotting of nicked plasmids, revealing that ATP hydrolysis and the non-SMC condensins are not required to compact DNA chirally. The second assay measured Smc2/4-dependent changes in linking number (Lk). Smc2/4 did not induce (+) supercoiling, but instead induced broadening of topoisomer distributions in a cooperative manner without altering Lk(0). To explain chiral knotting in substrates devoid of chiral supercoiling, we propose that Smc2/4 directs chiral DNA compaction by constraining the duplex to retrace its own path. In this highly cooperative process, both (+) and (-) loops are sequestered (about one per kb), leaving net writhe and twist unchanged while broadening Lk. We have developed a quantitative theory to account for these results. Additionally, we have shown at higher molar stoichiometries that Smc2/4 prevents relaxation by topoisomerase I and nick closure by DNA ligase, indicating that Smc2/4 can saturate DNA. By electron microscopy of Smc2/4-DNA complexes, we observed primarily two protein-laden bound species: long flexible filaments and uniform rings or "doughnuts." Close packing of Smc2/4 on DNA explains the substrate protection we observed. Our results support the hypothesis that SMC proteins bind multiple DNA duplexes.