  The deconfinement phase transition at high baryon densities and low
temperatures evades a direct investigation by means of lattice gauge
calculations. In order to make this regime of QCD accessible by computer
simulations, two proposal are made: (i) A Lattice Effective Theory (LET) is
designed which incorporates gluon and diquark fields. The deconfinement
transition takes place when the diquark fields undergo Bose-Einstein
condensation. (ii) Rather than using eigenstates of the particle number
operator, I propose to perform simulations for a fixed expectation value of the
baryonic Noether current. This approach changes the view onto the finite
density regime, but evades the sign and overlap problems. The latter proposal
is exemplified for the LET: Although the transition from the confinement to the
condensate phase is first order in the coupling constant space at zero baryon
densities, the transition at finite densities appears to be a crossover.
