Computations in anisotropic media are commonly simplified by applying perturbation methods. These require suitable background media, that are often chosen to be isotropic. In this paper we present expressions for sectorially best-fitting isotropic P- and S-velocities. The equations follow from a generalisation of Fedorov's (1968) technique. Examples for media with polar (VTI) and triclinic symmetry confirm the superiority of the results over the commonly used globally best-fitting isotropic velocities by Fedorov (1968). This makes the method particularly suited for any application associated with perturbation techniques for anisotropic wave propagation.