During the four most recent glacial cycles, atmospheric CO2 during glacial maxima has been lowered by about 90-100 ppm with respect to interglacials. There is widespread consensus that most of this carbon was partitioned in the ocean. It is, however, still debated which processes were dominant in achieving this increased carbon storage. In this paper, we use an Earth system model of intermediate complexity to explore the sensitivity of ocean carbon storage to ocean circulation state. We carry out a set of simulations in which we run the model to pre-industrial equilibrium, but in which we achieve different states of ocean circulation by changing forcing parameters such as wind stress, ocean diffusivity and atmospheric heat diffusivity. As a consequence, the ensemble members also have different ocean carbon reservoirs, global ocean average temperatures, biological pump efficiencies and conditions for air-sea CO2 disequilibrium. We analyse changes in total ocean carbon storage and separate it into contributions by the solubility pump, the biological pump and the CO2 disequilibrium component. We also relate these contributions to differences in the strength of the ocean overturning circulation. Depending on which ocean forcing parameter is tuned, the origin of the change in carbon storage is different. When wind stress or ocean diapycnal diffusivity is changed, the response of the biological pump gives the most important effect on ocean carbon storage, whereas when atmospheric heat diffusivity or ocean isopycnal diffusivity is changed, the solubility pump and the disequilibrium component are also important and sometimes dominant. Despite this complexity, we obtain a negative linear relationship between total ocean carbon and the combined strength of the northern and southern overturning cells. This relationship is robust to different reservoirs dominating the response to different forcing mechanisms. Finally, we conduct a drawdown experiment in which we investigate the capacity for increased carbon storage by artificially maximising the efficiency of the biological pump in our ensemble members. We conclude that different initial states for an ocean model result in different capacities for ocean carbon storage due to differences in the ocean circulation state and the origin of the carbon in the initial ocean carbon reservoir. This could explain why it is difficult to achieve comparable responses of the ocean carbon pumps in model intercomparison studies in which the initial states vary between models. We show that this effect of the initial state is quantifiable. The drawdown experiment highlights the importance of the strength of the biological pump in the control state for model studies of increased biological efficiency.