Collisions of deformed uranium nuclei are studied in a Monte-Carlo Glauber model. For U+U at zero impact parameter (b=0) in the most favorable orientation (tip-to-tip), the transverse particle density (charged-particle rapidity density per weighted transverse area of the initial participant zone) increases by about 35% compared to Au+Au at b=0. To estimate the advantage of U+U over Au+Au in the context of real experiments at the Relativistic Heavy Ion Collider, we examine the effect of a range of centrality cuts on the event sample. In terms of the transverse particle density, the predicted advantage of U+U is about 16%.