Based on the model of Paillard and Parrenin (2004), several box models that incorporate simple parameterizations of the oceanic CO2 pump were developed. The models’ parameters are calibrated to the ∂18O and CO2 observational time series available for the last 800 kyr BP. The Paillard model performance may be improved if its CO2 sensitivity to insolation is eliminated and different response times are assumed both for absorption/emission of CO2 and for ablation/accumulation of ice. With these changes the correlations between simulated and experimental time series increase from 0.59 and 0.63 (for CO2 and ice volume V) to 0.77 and 0.88 respectively. Oceanic CO2 pulses of 10 to 20 kyr are found to take place at the beginning of the last nine deglaciations according to this model. The timing of the last nine terminations may also be qualitatively reproduced with a primary production model in which export depends on V. The dependence between CO2 export and V that generates the best fit is not exponential, as expected from some evidences, but a square function. The good model-data fitting suggests that the rate of formation of deep water may be an important factor controlling the oceanic pulse that triggers the deglaciations.