The internal structure of oil-in-water microemulsion droplets has been studied by small-angle neutron scattering (SANS) using contrast variation. The single-chain surfactant used was N,N-dimethyldodecylamine-N-oxide (C(12)AO), and the oil phase was one of two semipolar ethyl esters, ethyl hexadecanoate or ethyl octanoate. Data from core-shell-drop neutron contrast series were simultaneously fitted to an interacting, polydisperse, core-shell, sphere model to investigate the possibility that the semipolar oils penetrate the curved surfactant film. For microemulsions containing a weight ratio of 1:5 ethyl hexadecanoate/surfactant, the data were most consistent with only a small extent of oil in the surfactant hydrocarbon (tail) region (similar to4% v/v), whereas in microemulsions containing the same amount of ethyl octanoate, the oil concentration was similar to 16% v/v. Increasing the relative amount of ethyl octanoate to 3:5 increased the extent of oil in the tail region to about 26% v/v. These results indicate that the extent of oil penetration into such positively curved monolayers depends on both the acyl chain length of the oil and its concentration. SANS data were also obtained for micelles of C(12)AO in D2O. Model fitting showed the micelles to be consistent with prolate ellipsoids having an axial ratio of around 1.6 to 1.7, Details of the model discussed do not entirely agree with models proposed in earlier literature. In both micelles and microemulsions, the surfactant behaves as if it has a small net charge, leading to repulsive rather than hard-sphere interactions.