The famous hyperbolic approximation of P-wave reflection moveout is strictly accurate only if the reflector is a plane, and the medium is homogeneous and isotropic. Heterogeneity, reflector curvature, and anisotropy are the three possible causes of moveout nonhyperbolicity at large offsets. In this paper, we analyze the situations where anisotropy is coupled with one of the other two effects. Using the weak anisotropy assumption for transversely isotropic media, we perform analytical derivations and comparisons. Both the case of vertical heterogeneity and the case of a curved reflector can be interpreted in terms of an effective anisotropy, though their anisotropic effects are inherently different from the effect of a homogeneous transversely isotropic model.