We explore the impact of three-dimensional minimum travel time ray tracing on nonlinear teleseismic inversion. This problem has particular significance when trying to image strongly contrasting low-velocity bodies, such as magma chambers, because strongly refracted and/or diffracted rays may precede the direct P wave arrival traditionally used in straight-ray seismic tomography. We use a simplex-based ray tracer to compute the three-dimensional, minimum travel time ray paths and employ an iterative inversion technique to cope with nonlinearity. Results from synthetic data show that our algorithm results in better model reconstructions compared with traditional straight-ray inversions. We reexamine the teleseismic data collected at Long Valley caldera by the U. S. Geological Survey. The most prominent feature of our result is a 25--30% low-velocity zone centered at 11.5 km depth beneath the northwestern quadrant of the caldera. Beneath this at a depth of 24.5 km is a more diffuse 15% low-velocity zone. In general, the low velocities tend to deepen to the south and east. We interpret the shallow feature to be the residual Long Valley caldera magma chamber, while the deeper feature may represent basaltic magmas ponded in the midcrust. The deeper position of the prominent low-velocity region in comparison to earlier tomographic images is a result of using three-dimensional rays rather than straight rays in our ray tracing. The magnitude of our low-velocity anomaly is a factor of ~3 times larger than earlier models from linear arrival time inversions and is consistent with models based on observations of ray bending at sites within the caldera. Our results imply the presence of anywhere from 7 to 100% partial melt beneath the caldera. ¿ American Geophysical Union 1995.