Aqueous single-walled carbon nanotube dispersions are often made using polymers from the pluronic family of amphiphilic block copolymers; however, relatively few studies have been conducted using small-angle neutron scattering techniques to discover the mechanism by which they act. SANS results reported here show that a relatively simple core-shell cylinder model can be used to fit data successfully at different contrasts. The results across all contrasts showed that the best fit gave an inner nanotube radius of 10 angstrom, corresponding to small nanotube bundles with a small amount of water present (20%), and a polydisperse adsorbed layer thickness of 61 angstrom, with a water content of 94% in the adsorbed layer. The data fitting is thus consistent with a small SWCNT bundle surrounded by an extended and water-swollen F127 adsorbed layer. Comparing the scattering from F127/SWCNT at different contrasts, it has been found that the polymer-decorated SWCNTs are contrast matched at a D2O/H2O volume ratio of 0.36:0.64, corresponding to a scattering-length density of 1.92 x 10(-6) angstrom(-2).