  We propose and analyse a scheme to cool atoms in an optical lattice to
ultra-low temperatures within a Bloch band, and away from commensurate filling.
The protocol is inspired by ideas from dark state laser cooling, but replaces
electronic states with motional levels, and spontaneous emission of photons by
emission of phonons into a Bose-Einstein condensate, in which the lattice is
immersed. In our model, achievable temperatures correspond to a small fraction
of the Bloch band width, and are much lower than the reservoir temperature.
