Currently TTI (transversely isotropic with a tilted symmetry axis) models are widely used for velocity analysis and imaging in many exploration areas. We develop a 3D parameter-estimation algorithm for TTI media composed of homogeneous layers separated by plane dipping interfaces. The input data include P-wave NMO ellipses and time slopes (horizontal slownesses of the zero-offset rays) combined with borehole information. If the symmetry axis is perpendicular to the bottom of each layer, it is possible to estimate the interval symmetry-direction velocity VP0, anisotropy parameter δ, and the reflector orientation using a single constraint — the reflector depth. The algorithm can tolerate small (≤ 5 ∘) deviation of the symmetry axis from the reflector normal. However, as is the case for the 2D problem, the parameter ɛ can seldom be obtained without nonhyperbolic moveout inversion. If the symmetry axis deviates from the reflector normal but is confined to the dip plane, stable parameter estimation requires specifying a relationship between the tilt and dip in each layer. When the tilt represents a free parameter, the input data have to be supplemented by wide-azimuth VSP traveltimes with the offset reaching at least 1/4 of the maximum reflector depth. Moreover, the additional angle coverage provided by VSP data may help resolve the parameter ɛ in the upper part of the model. The developed methodology can be used to build an accurate initial anisotropic velocity model for processing of wide-azimuth surveys.