  We analyse the phase diagram of ultra-cold bosons in a one-dimensional
superlattice potential with disorder using the time evolving block decimation
algorithm for infinite sized systems (iTEBD). For degenerate potential energies
within the unit cell of the superlattice loophole-shaped insulating phases with
non-integer filling emerge with a particle-hole gap proportional to the boson
hopping. Adding a small amount of disorder destroys this gap. For not too large
disorder the loophole Mott regions detach from the axis of vanishing hopping
giving rise to insulating islands. Thus the system shows a transition from a
compressible Bose-glass to a Mott-insulating phase with increasing hopping
amplitude. We present a straight forward effective model for the dynamics
within a unit cell which provides a simple explanation for the emergence of
Mott-insulating islands. In particular it gives rather accurate predictions for
the inner critical point of the Bose-glass to Mott-insulator transition.
