We establish the requisite design for arylene-ethynylene polymers that give rise to single-handed helical wrapping of single-walled carbon nanotubes (SWNTs). Highly charged semiconducting polymers that utilize either an (R)- or (S)-1,1'-bi-2-naphthol component in their respective conjugated backbones manifest HRTEM and AFM images of single-chain-wrapped SWNTs that reveal significant preferences for the anticipated helical wrapping handedness; statistical analysis of these images, however, indicates that similar to 20% of the helical structures are formed with the "unexpected" handedness. CD spectroscopic data, coupled with TDDFT-based computational studies that correlate the spectral signatures of semiconducting polymer-wrapped SWNT assemblies with the structural properties of the chiral 1,1'-binaphthyl unit, suggest strongly that two distinct binaphthalene SWNT binding modes, cisoid-facial and cisoid-side, are possible for these polymers, with the latter mode responsible for inversion of helical chirality and the population of polymer-SWNT superstructures that feature the unexpected polymer helical wrapping chirality at the nanotube surface. Analogous aryleneethynylene polymers were synthesized that feature a 2,2'-(1,3-benzyloxy)-bridged (b)-1,1'-bi-2-naphthol unit: this 1,1'-bi-2-naphthol derivative is characterized by a bridging 2,2'-1,3 benzyloxy tether that restricts the torsional angle between the two naphthalene subunits along its C1-C1' chirality axis to larger, oblique angles that facilitate more extensive van der Waals contact of the naphthyl subunits with the nanotube. Similar microscopic, spectroscopic, and computational studies determine that chiral polymers based on conformationally restricted transoid binaphthyl units direct preferential facial binding of the polymer with the SWNT and thereby guarantee helically wrapped polymer-nanotube superstructures of fixed helical chirality. Molecular dynamics simulations provide an integrated picture tying together the global helical superstructure and conformational properties of the binaphthyl units: a robust, persistent helical handedness is preferred for the conformationally restricted transoid binaphthalene polymer. Further examples of similar semiconducting polymer-SWNT superstructures are reported that demonstrate that the combination of single-handed helical wrapping and electronic structural modification of the conjugated polymer motif opens up new opportunities for engineering the electro-optic functionality of nanoscale objects.