Quasar absorption lines provide a precise test of whether the fine-structure constant, {alpha}, is the same in different places and through cosmological time. We present a new analysis of a large sample of quasar absorption-line spectra obtained using the Ultraviolet and Visual Echelle Spectrograph (UVES) on the Very Large Telescope (VLT) in Chile. We apply the many-multiplet method to derive values of {DELTA}{alpha}/{alpha}==({alpha}z-{alpha}0)/{alpha}0 from 154 absorbers, and combine these values with 141 values from previous observations at the Keck Observatory in Hawaii.