The covalent grafting of polymers to single-walled carbon nanotubes (SWCNTs) is widely used to improve solvent compatibility, as well as composite and functional performance. Here, three different graft-to strategies are directly compared, using azide, diazonium, and bromide terminated polymers, over four different molecular weights (oligomeric to 10 kDa) using specifically synthesized low polydispersity, end-group controlled poly(vinyl acetate) (PVAc) prepared by polymerisation using a bespoke protected-amine RAFT agent. Coupling of the bromo-polymer to reduced SWCNTs led to higher degrees of functionalisation (grafting ratios up to 68.9%) than the azide and diazonium grafting reactions, attributed to better initial dispersion of the pre-grafted SWCNTs. The use of higher molecular weight polymers led to a decrease in the total weight of polymer grafted, as the increase in per-polymer weight is more than offset by steric occlusion on the SWCNT surface. For these graft-to reactions, the dispersibility of grafted SWCNTs was found to depend most strongly on the polymer molecular weight, not total weight of grafted polymer or grafting chemistry, with an intermediate Mn∼5757 PVAc giving the best dispersibilities, at up to 118 mg L−1.