Recent observational evidence of upwelling-mantle anisotropy at a slow spreading center has motivated the modeling of teleseismic arrivals at mid-ocean ridges. The models consider a variety of types of anisotropy and heterogeneity where the emphasis is to ascertain whether or not travel-times can be used to discriminate between the existence of partial melt and anisotropy. Two mechanisms for anisotropy in the upwelling asthenosphere are considered: one due to the preferential alignment of the fast axes of olivine crystals in the direction of mantle flow and the other due to the preferential alignment of cracks that feed melt towards the spreading axis. The results indicate that P-waves are most sensitive to even modest amounts of flow-induced asthenospheric anisotropy, while S-waves are most sensitive to the presence of mantle melt. Multiple S-wave arrivals are predicted for many models, most notably the ones with anisotropy due to crack-alignment where very large S-wave separations develop. The model which best fits existing data requires a higher degree of crystal-alignment anisotropy in the upwelling-asthenosphere than in the lithosphere. This effect has been predicted in studies of the evolution of crystal-alignment anisotropy in polycrystalline aggregates.