In this study we present new constraints on the nature of the low-velocity zone beneath Long Valley caldera, based on the measured propagation directions of teleseismic P waves and on modeling of P to S converted waves. The low-velocity body is a large asymmetrical volume which deepens to the east, extending from depths of 7 to 30 km. It contains lower velocities than originally proposed by earlier teleseismic studies. In particular, there is a tabular feature between 7 and 11 km depth that has a reduction in velocity of about 30%. These low velocities imply a much greater percentage of melt in the crust beneath Long Valley caldera than previously estimated. Array analysis of large delayed arrivals identifies them to be Ps converted waves from the shoulders and roof of this tabular zone. These conversions bound the depth to the magma chamber roof to be within about 10 km of the surface. Our results are consistent with elements from several other studies, and we present an integrated and improved model of crustal structure at Long Valley. The concordance of the deeper low-velocity zones with regional structural trends implies that the shallow low-velocity feature is a cupola on top of an asymmetric diapiric ridge rising up from the migmatized lower crust of the Basin and Range. We present two contrasting interpretations of the geometry of low-velocity zones in the crust: one implies a time-invariant magma chamber and conduit system for Long Valley caldera, the other implies an evolution of that system from a simple vertical regime to its current asymmetrical geometry.