Mixtures of tetraethylammonium perfluorooctylsulfonate (TEAFOS) and lithium perfluorooctylsulfonate (LiFOS) in water (D2O) are studied as a function of the LiFOS fraction (phi(Li)) at a total concentration of 100 mM and 30 degrees C by means of H-1 and F-19 NMR and viscosity measurements. The counterion binding in the double layer structure of the FOS micelles is analyzed through the chemical shifts and self-diffusion coefficients that are sensitive to the Stem and diffuse double layers, respectively. At phi(Li) = 0, the fraction of bound tetraethylammonium counterions (TEA(+)) due to the proton chemical shift is found to be 0.45; it implies that one TEA(+) counterion is bound to and bridging roughly two micellized FOS-ions. This value is markedly smaller than that (0.73) obtained by the diffusion data because of the short-range sensitivity of the chemical shift. The binding fraction due to the diffusion data is higher because it involves both the Stern and diffuse double layers. The concentration of the TEA(+) counterions preferentially localized within the Stern layer remains constant at 45 mM when phi(Li) is varied between 0 and 0.55. It is shown that the preferential saturation of the Stern layer with TEA(+) counterions in this region of phi(Li) is prerequisite for the formation of the threadlike FOS structure and the high solution viscosity. At higher values of phi(Li), the threadlike structure disintegrates and the viscosity drops as a result of an overall shortage of TEA(+) counterions in the solution.