Aqueous dispersions of single-walled carbon nanotubes are often made using sodium dodecylsulfate (SDS), which adsorbs to the nanotube surface to stabilise them. Despite SDS being commonly used with single-walled carbon nanotubes, there is no consensus on the structure of the adsorbed layer. Small-angle neutron and X-ray scattering results reported here show that the data can be fitted to a relatively simple core-shell cylinder model, consistent with a polydisperse nanotube core of radius 10 A, surrounded by an adsorbed surfactant layer of thickness 18 angstrom and volume fraction of 0.5. This is consistent with small nanotube bundles surrounded by an adsorbed layer of extended SDS molecules. (C) 2016 The Authors. Published by Elsevier Inc.