Tremendous progress has been made to stabilize carbon nanotube dispersions using surfactants, although many questions await answer to design surfactant formulations that selectively stabilize nanotubes mono-dispersed in diameter and chirality. Stimulated by recent experimental observations [J. Am. Chem. Soc., 2010, 132, 16165–16175], we attempt here to quantify how changing the counter-ion (Cs+ instead of Na+) affects the morphology of dodecyl sulfate surfactants adsorbed on carbon nanotubes. Using atomistic molecular dynamics we simulated aqueous cesium dodecyl sulfate (CsDS) adsorbed on (6,6), (12,12), and (20,20) single-walled carbon nanotubes (SWCNTs) at ambient conditions. When compared to results for sodium dodecyl sulfate (SDS), our results suggest that surface aggregates with Cs+ ions, compared to Na+, yield a more compact coverage of the nanotubes at the surfactant surface coverage of 0.25 nm2 per headgroup, with the surfactant heads extended towards the bulk aqueous solution, and prevent water from accessing the nanotube surface. These morphological results suggest that CsDS should be more effective than SDS at stabilizing aqueous carbon nanotubes dispersions. More importantly, these results were obtained only for the (6,6) nanotubes simulated. For the wider nanotubes our simulations show limited, if any, differences in the morphology of the surfactant aggregates when the Na+ ions are substituted with Cs+ ones. To validate our results we measured experimental UV-Vis-NIR absorbance spectra for aqueous carbon nanotubes with diameters similar to that of (6,6) and of (12,12) nanotubes stabilized by SDS at increasing salt concentration (CsCl vs. NaCl). The results are indicative of changes in the surfactant self-assembled structure on the narrow nanotubes in the presence of Cs+ ions, while data for the wider tubes only suggest salt-screening effects for both Na+ and Cs+ ions. The different salt-specific behavior observed for the surfactants adsorbed on narrow vs. wide carbon nanotubes could be exploited for the selective stabilization of mono-dispersed carbon nanotube samples, although a surfactant more effective than SDS should be used.