A carbon cycle model is described incorporating CO2 fertilization feedback and a convolution ocean model that allows the atmosphere-to-ocean flux to be varied. The main parameters controlling the model's behaviour are a fertilization feedback parameter (r) and an ocean flux scaling factor (characterized by the mean carbon flux into the ocean over the 1980s, F(1980s)). Since the model's 1980s-mean net land-use-change flux (Dn(1980s)) is a unique function of r and F(1980s), the model's behaviour can also be characterized by specifying Dn(1980s) (instead of r) and F(1980s). The history of past land-use fluxes, Dn (t), is derived by inverse modelling for a range of values of F(1980s) (1.0–3.0 GtC/yr) and Dn(1980s) (0.6–2.6 GtC/yr). Even with this flexibility, the resultant Dn(t) differs markedly from the observationally-based record of Houghton, particularly before 1950. The inverse calculations are used to determine the history of the so-called “missing sink”, as implied directly by the model and by the observationally-based record of Dn(t), for a range of ocean uptake efficiencies as defined by F(1980s). Projections of future CO2 concentration changes are made for the 6 emissions scenarios recently produced by the Intergovernmental Panel on Climate Change (IS92a–f). The ability to specify F(1980s) and Dn(1980s) allows one to account for the missing sink in a variety of ways, and to account for uncertainties in the amount of missing carbon. This leads to a range of projections and provides some insights into the uncertainties surrounding these projections.