To better understand the contributions that the structural maintenance of chromosome proteins (SMCs) make to condensin activity, we have tested a number of biochemical, biophysical, and DNA-associated attributes of the Smc2p-Smc4p pair from budding yeast. Smc2p and Smc4p form a stable heterodimer, the "Smc2/4 complex," which upon analysis by sedimentation equilibrium appears to reversibly self-associate to form heterotetramers. Individually, neither Smc2p nor Smc4p hydrolyzes ATP; however, ATPase activity is recovered by equal molar mixing of both purified proteins. Hydrolysis activity is unaffected by the presence of DNA. Smc2/4 binds both linearized and circular plasmids, and the binding appears to be independent of adenylate nucleotide. High mole ratios of Smc2/4 to plasmid promote a geometric change in circular DNA that can be trapped as knots by type II topoisomerases but not as supercoils by a type I topoisomerase. Binding titration analyses reveal that two Smc2/4-DNA-bound states exist, one disrupted by and one resistant to salt challenge. Competition-displacement experiments show that Smc2/4-DNA-bound species formed at even high protein to DNA mole ratios remain reversible. Surprisingly, only linear and supercoiled DNA, not nicked-circular DNA, can completely displace Smc2/4 prebound to a labeled, nicked-circular DNA. To explain this geometry-dependent competition, we present two models of DNA binding by SMCs in which two DNA duplexes are captured within the inter-coil space of an Smc2/4 heterodimer. Based on these models, we propose a DNA displacement mechanism to explain how differences in geometry could affect the competitive potential of DNA.