TRACER-CALIBRATED models of the total uptake of anthropogenic CO2 by the world's oceans give estimates of about 2 gigatonnes carbon per year1, significantly larger than a recent estimate2 of 0.3-0.8 Gt C yr-1 for the synoptic air-to-sea CO2 influx. Although both estimates require that the global CO2 budget must be balanced by a large unknown terrestrial sink, the latter estimate implies a much larger terrestrial sink, and challenges the ocean model calculations on which previous CO2 budgets were based. The discrepancy is due in part to the net flux of carbon to the ocean by rivers and rain, which must be added to the synoptic air-to-sea CO2 flux to obtain the total oceanic uptake of anthropogenic CO2. Here we estimate the magnitude of this correction and of several other recently proposed adjustments to the synoptic air-sea CO2 exchange. These combined adjustments minimize the apparent inconsistency, and restore estimates of the terrestrial sink to values implied by the modelled oceanic uptake.