Global phase velocity maps of long-period surface waves are an essential ingredient in modeling 3-D shear wave velocity and are capable of particularly good lateral resolution of upper mantle structure. Unfortunately, even recently derived maps disagree for harmonic degrees greater than about 6 so that further improvement is required. The resolution can be dramatically improved by adding both amplitude and polarization data to the inversion process. Both amplitude and polarization depend on the lateral gradients of phase velocity and hence constrain the short-wavelength structure of the resulting models. Amplitude, polarization, and phase are readily determined for each arriving wave packet using multitaper techniques and can be interpreted using linear perturbation theory. The size of our phase and polarization data sets obtained from seismograms of the global seismic broadband networks GEOSCOPE, IDA/IRIS (International Deployment of Accelerometers/Incorporate Research Institutions for Seismology) and IRIS/USGS (U.S. Geological Survey) justifies inversion for phase velocity expanded in spherical harmonics up to l=24. While the phase data between 3 and 15 mHz do not require structure beyond about l=8, small-amplitude structure of harmonic degree greater than 8 is needed to fit the polarization data. Checkerboard tests show that the resolution of phase velocity is greatly improved when polarization data are added to the inversion. Since amplitude data also depend on 3-D anelastic structure of the mantle, these data need a more comprehensive interpretation, and we cannot expect to fit them with a purely elastic model. However, in this paper we show that a good fraction of the amplitude signal is consistent with our phase velocity maps and that it is possible to obtain maps which simultaneously explain both amplitude and polarization data. ¿ American Geophysical Union 1996