Q values for the direct Lg phase () were estimated for event-station paths that lie entirely within the western United States, particularly in the southern Great Basin and surrounding areas. The Qo ( at 1 Hz) values were estimated by fitting synthetic spectra to observed Lg spectra using a genetic algorithm technique. We have created a tomographic image of the variations of Qo for a part of the southwestern United States. The image shows that Qo varies between about 234 and 312 at 1 Hz, with an average of 267. The lowest Qo occurs in the northwest part of the Basin and Range Province, where extensional deformation has occurred since the Mesozoic. Qo values start to increase toward the Colorado Plateau to the east and continue to gradually increase northward and decrease southward. We also find relatively high frequency dependence to the values, with a 1D mean of η = 0.57.