Traveltime tomography relies on broad ray-angle coverage to constrain the spatial location of velocity anomalies. When ray-angle coverage is narrow, cell or grid tomography can be plagued by smearing artifacts bearing imprints of the raypaths. Multiscale deformable-layer tomography (DLT), which inverts for the geometry of velocity interfaces instead of velocity, can be more effective than grid-based tomography in mitigating such artifacts, especially when velocity values are known for parts of the model. The DLT model consists of geologically sensible layers represented by triangular prisms. In areas of good ray coverage, DLT can be used to invert simultaneously for layer velocities as well as interface geometry. Tests of synthetic models of crosswell refraction, 2D tomostatics, and 3D vertical seismic profiling (VSP) first-arrival data sets show that DLT can produce solutions superior to those produced by cell- or grid-based tomography.