We use International Seismological Centre (ISC) P arrival data (1964--1987) and iterative algorithms which minimize the l1 and l2 residual norms to solve simultaneously for three-dimensional P velocity variations in Earth's mantle,source mislocations, and station corrections. We find that the maximum velocity perturbations produced by the l1 minimization (approximately ¿4% in our final model) are relatively insensitive to smoothing and damping constraints. Therefore, using an l1 norm criterion allows us to keep the bias introduced to the inversion to a minimum. Among the well-resolved features contained in both the l1 and velocity models are a fast anomaly in the lower mantle beneath the Tonga-New Hebrides subduction zone to a depth of 1670 km and another fast anomaly beneath the Japanese island arc and eastern Asia. Continuity between these anomalies and shallower fast anomalies is not clear. A fast anomaly extending from 670 km to 2070 km depth appears beneath eastern North America, the Caribbean, and north central South America. A broad, fast anomaly appears beneath eastern Asia just above the core-mantle boundary as well as several slow anomalies under the Pacific basin of comparable size. Both models contain a circum-Pacific ring of 2% lower velocities in the depth range 0--200 km, associated with back arc basins. High velocities (over 2%) associated with the continental shields tend to disappear below 400 km, though a significant region of high velocity remains beneath the Siberian platform in the 400 to 670 km depth interval. ¿American Geophysical Union 1993