  We report measurements on MgB2 up to ~40GPa. Increasing pressure yields a
monotonous decrease of the lattice parameters and of the c/a ratio, but no
structural transition down to parameters smaller than those of AlB2. The
transition superconducting temperature also decreases with temperature in a
sample dependent way. The results are explained by an increase of the filling
of the 2D pxy bands with pressure, the Mg stoichiometry determining the
starting position of the Fermi level. Our measurements indicate that these hole
bands are the relevant ones for superconductivity.
