With a widely available magnetic field of 10 T, one can attain the quantum limit in bismuth and graphite. At zero magnetic field, these two elemental semi-metals host a dilute liquid of carriers of both signs. All quasi-particles are confined to a few Landau tubes, when the quantum limit is attained. Each time a Landau tube is squeezed before definitely leaving the Fermi surface, the Nernst response sharply peaks. For bismuth, additional Nernst peaks, unexpected in the non-interacting picture, are resolved beyond the quantum limit. The amplitudes of these unexpected Nernst peaks become more pronounced for the samples with the longest electron mean free path.