  We report measurements of the de Haas-van Alphen effect for single crystals
of MgB$_2$, in magnetic fields up to 32 Tesla. In contrast to our earlier work,
dHvA orbits from all four sheets of the Fermi surface were detected. Our
results are in good overall agreement with calculations of the electronic
structure and the electron-phonon mass enhancements of the various orbits, but
there are some small quantitative discrepancies. In particular, systematic
differences in the relative volumes of the Fermi surface sheets and the
magnitudes of the electron-phonon coupling constants could be large enough to
affect detailed calculations of T$_{c}$ and other superconducting properties.

Superconductivity