The effect of added oil on the local structure of oil-swollen cylindrical micelles in the system C12E5 + decane + water was investigated by small-angle neutron scattering (SANS). The geometry of the aggregates was studied for fixed overall concentration of surfactant plus oil, c(m)=7 mg/mL, and increasing oil content alpha (the mass fraction of oil in the dispersed mixture of surfactant plus oil), to clarify the dependency of the apparent molar mass on alpha which was observed in a preceding light scattering study (J. Phys. Chem. B 1999, 103, 5768). There it was found that with increasing alpha at given cm the molar mass of the micelles increases up to a maximum near alpha=0.07 and then decreases sharply as the oil content is further increased. The present work shows that this decrease of the molar mass results from a decrease of the micellar contour length L-c, whereas the mass per unit length M-L of the aggregates increases almost linearly over the entire range of oil content.