Single sodium beacons will likely be the most convenient for adaptive systems to correct 6 - 10 m class telescopes over a small field of view (the isoplanatic angle), provided reliable, powerful 589 nm lasers become available and affordable. However, when adaptive optics are applied to extended fields of view and correction of telescopes as large as 32 m diameter, it seems likely that laser beacons produced by Rayleigh scattering will be preferred. For these more demanding applications which require atmospheric tomography, Rayleigh beacons come into their own for two reasons. First, the cone effect, which causes the high turbulence to be sampled at a different scale, is no longer problematic when multiple lasers are used and height dependence is solved for explicitly. Second, the tomographic solution can make use of the beacon created by a laser pulse during all of its journey through the upper atmosphere, not just scattering from a thin layer selected by range gating. In this way a laser that costs an order of magnitude less to buy and maintain than a sodium laser of the same power can yield a brighter beacon and more information about the atmospheric turbulence. This is important because both the number and brightness of beacons or stars must increase with the number of layers included in the tomographic solution. For the same reason, tomography with natural stars is unlikely to be valuable for very large telescopes because in general the number and required brightness of each star increase with corrected field angle, while current narrow-field adaptive optics systems relying on natural stars are already very limited in sky coverage. Our method for tomography to take advantage of Rayleigh scattering over a wide range of heights uses short pulses from near diffraction-limited, ultraviolet lasers, projected from a small aperture above the telescope's secondary mirror. Each pulse subtends less than 1 arcsec at any instant as it travels up through many kilometers. An imaging detector at the main telescope focus conjugate to mid-height is used to record fast movies of the rising pulses as they come into and out of focus. Phase diversity analysis of the movies taken together then yields the three-dimensional turbulence of the atmosphere.