The underdetermination of theory by data argument (UD) is traditionally construed as an argument that tells us that we ought to favour an anti-realist position over a realist position. I argue that when UD is constructed as an argument saying that theory choice is to proceed between theories that are empirically equivalent and adequate to the phenomena up until now, the argument will not favour constructive empiricism over realism. A constructive empiricist cannot account for why scientists are reasonable in expecting one theory to be empirically adequate rather than another, given the criteria he suggests for theory choice.