Solubilizing and purifying carbon nanotubes remains one of the foremost technological hurdles in their investigation and application. We report a dramatic improvement in the preparation of single-walled carbon nanotube solutions based on the ability of specific aromatic polymers to efficiently disperse certain nanotube species with a high degree of selectivity. Evidence of this is provided by optical absorbance and photoluminescence excitation spectra, which show suspensions corresponding to up to similar to 60% relative concentration of a single species of isolated nanotubes with fluorescence quantum yields of up to 1.5%. Different polymers show the ability to discriminate between nanotube species in terms of either diameter or chiral angle. Modelling suggests that rigid-backbone polymers form ordered molecular structures surrounding the nanotubes with n-fold symmetry determined by the tube diameter.