Small-angle neutron scattering (SANS) and electron paramagnetic resonance (EPR) have been used to characterize mixed micelles comprising the anionic surfactant sodium dodecyl sulfate (SDS) and the sugar-based nonionic surfactant (tetradecylmalono)bis(N-methylglucamide) (C(14)BNMG). Parallel studies using protonated and deuterated SDS have permitted the calculation of the mole fraction of SDS in the micelle (x(SDS)). The size of the hydrophobic core of the mixed micelles is essentially invariant with mole fraction x(SDS). The volume of the polar shell containing the surfactant headgroups increases with decreasing x(SDS). The amount of water present in this shell can be obtained from knowledge of the shell volume and the number and volume of the two types of headgroup occupying the shell. Water comprises about 70% of the polar shell in SDS but is almost completely excluded from the headgroup region of micelles of the nonionic surfactant. EPR has also been used to determine the polarity index, which contains a contribution from the OH groups on the headgroup of the sugar surfactant as well as a contribution from the water. From the rotational correlation time of the spin-probe, a microviscosity has been calculated that increases with decreasing x(SDS), perhaps due to steric hindrance of the large glucamide groups or hydrogen bonding between them.