Box models of the ocean/atmosphere CO2 system rely on mechanisms at polar outcrops to alter the strength of the ocean's organic carbon pump. GCM-based carbon system models are reportedly less sensitive to the same processes. Here we separate the carbon pumps in a three-box model and the GCM-based Princeton Ocean Biogeochemistry Model to show how the organic pumps operate in the two kinds of models. The organic pumps are found to be quite different in two respects. Deep water in the three-box model is relatively well equilibrated with respect to the pCO2 of the atmosphere while deep water in the GCM tends to be poorly equilibrated. This makes the organic pump inherently stronger in the GCM than in the three-box model. The second difference has to do with the role of polar nutrient utilization. The organic pump in the GCM is shown to have natural upper and lower limits that are set by the initial PO4 concentrations in the deep water formed in the North Atlantic and Southern Ocean. The strength of the organic pump can swing between these limits in response to changes in deep-water formation that alter the mix of northern and southern deep water. Thus, unlike the situation in the three-box model, the organic pump in the GCM can become weaker or stronger without changes in polar nutrient utilization.