Physico-chemical methods to sort single-walled carbon nanotubes (SWNTs) by chiral index are presently lacking but are required for in-depth experimental analysis and also for potential future applications of specific species. Here we report the unexpected selectivity of poly(N-decyl-2,7-carbazole) to almost exclusively disperse semi-conducting SWNTs with differences of their chiral indices (n - m) >= 2 in toluene. The observed selectivity complements perfectly the dispersing features of the fluorene analogue poly(9,9-dialkyl-2,7-fluorene), which disperses semiconducting SWNTs with (n - m) <= 2 in toluene. The dispersed samples are further purified by density gradient centrifugation and analyzed by photoluminescence excitation spectroscopy. All-atom molecular modeling with decamer model compounds of the polymers and (10,2) and (7,6) SWNTs suggests differences in the pi-pi stacking interaction as origin of the selectivity. We observe energetically favored complexes between the (10,2) SWNT and the carbazole decamer and between the (7,6) SWNT and the fluorene decamer, respectively. These findings demonstrate that subtle structural changes of polymers lead to selective solvation of different families of carbon nanotubes. Furthermore, chemical screening of closely related polymers may pave the way toward simple, low-cost, and index-specific isolation of SWNTs.