We report the preparation and structural characterization of core/shell CdSe/CdS/ZnS nanorods. A graded shell of larger band gap is grown around CdSe rods using trioctylphosphine oxide as a surfactant. Interfacial segregation is used to preferentially deposit CdS near the core, providing relaxation of the strain at the core/shell interface. The reported synthesis allows for variation of the shell thickness between one and six monolayers, on core nanorods ranging from aspect ratios of 2:1 to 10:1. After an irreversible photochemical annealing process, the core/shell nanorods have increased quantum efficiencies and are stable in air under visible or UV excitation. In addition to their robust optical properties, these samples provide an opportunity for the study of the evolution of epitaxial strain as the shape of the core varies from nearly spherical to nearly cylindrical.