Transversely isotropic models with a tilted symmetry axis (TTI) play an increasingly important role in seismic imaging, especially near salt bodies and in active tectonic areas. Here, we present a 2D parameter-estimation methodology for TTI media based on combining P-wave normal-moveout (NMO) velocities, zero-offset traveltimes, and reflection time slopes with borehole data that include check-shot traveltimes as well as the reflector depths and dips. For a dipping TTI layer with the symmetry axis confined to the dip plane of the reflector, simultaneous estimation of the symmetry-direction velocity , the anisotropy parameters ϵ and δ, and the tilt ν of the symmetry axis proves to be ambiguous despite the borehole constraints. If the symmetry axis is orthogonal to the reflector, and δ can be recovered with high accuracy, even when the symmetry axis deviates by from the reflector normal. The parameter ϵ, however, cannot be constrained for dips smaller than 60° without using nonhyperbolic moveout. To invert for the interval parameters of layered TTI media, we apply 2D stacking-velocity inversion supplemented with the same borehole constraints. The dip planes in all layers are assumed to be aligned, and the symmetry axis is set orthogonal to the reflector in each layer. Information about reflector dips can be replaced with near-offset walkaway vertical seismic profiling (VSP) traveltimes. Tests on noise-contaminated data demonstrate that the algorithm produces stable estimates of the interval parameters and δ, if the range of dips does not exceed 30°. Our method can be used to build an accurate initial TTI model for post-migration reflection tomography and other techniques that employ migration velocity analysis.