The magnetic and electronic properties of non-Fermi liquid UCu_4Pd depend on annealing conditions. Local structural changes due to this annealing are reported from UL_III- and Pd K-edge x-ray absorption fine-structure measurements. In particular, annealing decreases the fraction of Pd atoms on nominally Cu 16$e$ sites and the U-Cu pair-distance distribution width. This study provides quantitative information on the amount of disorder in UCu_4Pd and allows an assessment of its possible importance to the observed non-Fermi liquid behavior.