One-dimensional colloidal multicomponent semiconductor nanorods, such as CdSe-CdS dot-in-rod, have been extensively studied as a promising class of new materials for solar energy conversion because of the possibilities of using the band alignment of component materials and the rod-diameter-dependent quantum confinement effect to control the location of electrons and holes and to incorporate catalysts through the growth of Pt tips. Here we used CdS nanorods as an example to study the effect of nonuniform diameters along the rod on the exciton localization and dissociation dynamics in CdS and (platinum tipped) CdS-Pt nanorods. We showed that, in CdS nanorods prepared by seeded growth, the presence of a bulb with a larger diameter around the CdS seed resulted in an additional absorption band lower in energy than the exciton in the CdS rod. As a result, excitons generated in the CdS rod could undergo ultrafast localization to the bulb region in addition to trapping on the CdS rod. We observed that the Pt tip led to fast exciton dissociation by electron transfer. However, excitons localized on the CdS bulb showed slower average ET rates than those localized in the rod region. Our findings suggested that the effect of rod morphology should be carefully considered in designing multicomponent nanorods for solar energy conversion applications.