  The phase diagram of the Bose-Hubbard model in the presence of off-diagonal
disorder is determined using Quantum Monte Carlo simulations. A sequence of
quantum glass phases intervene at the interface between the Mott insulating and
the Superfluid phases of the clean system. In addition to the standard Bose
glass phase, the coexistence of gapless and gapped regions close to the Mott
insulating phase leads to a novel Mott glass regime which is incompressible yet
gapless. Numerical evidence for the properties of these phases is given in
terms of global (compressibility, superfluid stiffness) and local
(compressibility, momentum distribution) observables.
