We used Hi-C, imaging, proteomics, and polymer modeling to define rules of engagement for SMC (structural maintenance of chromosomes) complexes as cells refold interphase chromatin into rod-shaped mitotic chromosomes. First, condensin disassembles interphase chromatin loop organization by evicting or displacing extrusive cohesin. Second, condensin bypasses cohesive cohesins, thereby maintaining sister chromatid cohesion as sisters separate. Studies of mitotic chromosomes formed by cohesin, condensin II, and condensin I alone or in combination lead to refined models of mitotic chromosome conformation. In these models, loops are consecutive and not overlapping, implying that condensins stall upon encountering each other. The dynamics of Hi-C interactions and chromosome morphology reveal that during prophase, loops are extruded in vivo at ∼1 to 3 kilobases per second by condensins as they form a disordered discontinuous helical scaffold within individual chromatids.