The molecular conductor eta-Mo4O11 undergoes two successive charge den
sity wave transitions at 109 K and 30 K, with corresponding changes in
the electronic structure. The resulting low temperature Fermi surface
has only very small closed orbits at the Fermi level, all of which re
ach the quantum limit by 20 T. We report high field, low temperature m
agnetoresistance studies in the low temperature state, including hydro
static pressure dependence.