  The consequences of disorder on interacting bosons trapped in optical
lattices are investigated by quantum Monte Carlo simulations. At small to
moderate strengths of potential disorder a unique effect is observed: if there
is a Mott plateau at the center of the trap in the clean limit, phase coherence
{\it increases} as a result of disorder. The localization effects due to
correlation and disorder compete against each other, resulting in a partial
delocalization of the particles in the Mott region, which in turn leads to
increased phase coherence. In the absence of a Mott plateau, this effect is
absent. A detailed analysis of the uniform system without a trap shows that the
disordered states participate in a Bose glass phase.
