Cohesin and condensin play fundamental roles in sister chromatid cohesion and chromosome segregation, respectively. Both consist of heterodimeric structural maintenance of chromosomes (SMC) subunits, which possess a head (containing ATPase) and a hinge, intervened by long coiled coils. Non-SMC subunits (Cnd1, Cnd2, and Cnd3 for condensin; Rad21, Psc3, and Mis4 for cohesin) bind to the SMC heads. Here, we report a large number of spontaneous extragenic suppressors for fission yeast condensin and cohesin mutants, and their sites were determined by whole-genome sequencing. Mutants of condensin's non-SMC subunits were rescued by impairing the SUMOylation pathway. Indeed, SUMOylation of Cnd2, Cnd3, and Cut3 occurs in midmitosis, and Cnd3 K870 SUMOylation functionally opposes Cnd subunits. In contrast, cohesin mutants  rad21  and  psc3  were rescued by loss of the RNA elimination pathway (Erh1, Mmi1, and Red1), and loader mutant  mis4  was rescued by loss of Hrp1-mediated chromatin remodeling. In addition, distinct regulations were discovered for condensin and cohesin hinge mutants. Mutations in the N-terminal helix bundle [containing a helix-turn-helix (HTH) motif] of kleisin subunits (Cnd2 and Rad21) rescue virtually identical hinge interface mutations in cohesin and condensin, respectively. These mutations may regulate kleisin's interaction with the coiled coil at the SMC head, thereby revealing a common, but previously unknown, suppression mechanism between the hinge and the kleisin N domain, which is required for successful chromosome segregation. We propose that in both condensin and cohesin, the head (or kleisin) and hinge may interact and collaboratively regulate the resulting coiled coils to hold and release chromosomal DNAs.