The displacement of a nonionic polymeric dispersant, Pluronic F127, adsorbed at the surface of single-walled carbon nanotubes, by low molecular-weight ionic dispersants (surfactants) is studied in aqueous dispersion. The method applied is diffusion NMR spectroscopy that can accurately measure the fraction of F127 molecules adsorbed at the tube surface because of the slow exchange (over the experimental time scale) of F127 between bulk and surface. In a series of surfactants with varying chain length and headgroups, we find that anionic surfactants replace in general more nonionic F127 than do cationic surfactants. The data collected show a strong correlation with the critical dispersibility concentration of the different surfactants, a parameter that signifies the concentration at which one obtains significant dispersed nanotube concentration by ultrasonication. We posit that this finding indicates the existence of a threshold surface coverage for dispersants that constitutes a necessary condition for de-bundling by ultrasonication. The results are discussed in relation to previous findings in the literature.