It is widely known that beams that have optical vortices along the direction of propagation can be easily created in the laboratory. However, it is less well known that it is possible to create beams that have vortices transversely through the beam waist. Despite much work on beams with parabolic trajectories the creation of beams with transverse vortices are not well understood. Recently such beams have been created in the laboratory with computer-generated holograms. Though such beams can be created relatively easily, optimization of the vortex structure requires generation of the correct kinoform for the optical system. Imprecise application of such kinoforms can generate multiple vortices at the beam focus, which may not be optimal in many experimental applications. In this paper, we discuss the properties of such beams and investigate the optimal geometry for creating beams with transverse vortices. Applications for beams with transverse vortices may exist in optical micromanipulation, quantum communications and microscopy.