We use an Earth system model of intermediate complexity, CLIMBER-2, to investigate what recent improvements in the representation of the physics and biology of the glacial ocean imply for the atmospheric concentration. The coupled atmosphere-ocean model under the glacial boundary conditions is able to reproduce the deep, salty, stagnant water mass inferred from Antarctic deep pore water data and the changing temperature of the entire deep ocean. When carbonate compensation is included in the model, we find a CO2 drawdown of 43 ppmv associated mainly with the shoaling of the Atlantic thermohaline circulation and an increased fraction of water masses of southern origin in the deep Atlantic. Fertilizing the Atlantic and Indian sectors of the Southern Ocean north of the polar front leads to a further drawdown of 37 ppmv. Other changes to the glacial carbon cycle include a decrease in the amount of carbon stored in the terrestrial biosphere (540 Pg C), which increases atmospheric CO2 by 15 ppmv, and a change in ocean salinity resulting from a drop in sea level, which elevates CO2 by another 12 ppmv. A decrease in shallow water CaCO3 deposition draws down CO2 by 12 ppmv. In total, the model is able to explain more than two thirds (65 ppmv) of the glacial to interglacial CO2 change, based only on mechanisms that are clearly documented in the proxy data. A good match between simulated and reconstructed distribution of δ13C changes in the deep Atlantic suggests that the model captures the mechanisms of reorganization of biogeochemistry in the Atlantic Ocean reasonably well. Additional, poorly constrained mechanisms to explain the rest of the observed drawdown include changes in the organic carbon:CaCO3 ratio of sediment rain reaching the seafloor, iron fertilization in the subantarctic Pacific Ocean, and changes in terrestrial weathering.