A new method for deconvolving ice core CO2 and δ13CO2 measurements to estimate net CO2 uptake by the terrestrial biosphere and the oceans has been developed. The method, which uses the Kalman filter, incorporates statistical analysis into the calculation. This allows a more rigorous analysis of CO2 variability than the usual deconvolution method. The Kalman filter method estimates uncertainties on the deduced fluxes as part of the calculation. The deconvolution method is applied to the Law Dome CO2 and δ13C ice core record. The calculation suggests that natural variability in CO2 fluxes may be as large as 1 GtC yr-1 (GtC is gigatonnes carbon, 1 Gt = 1015 g) on the timescale of just less than a decade. The Law Dome CO2 measurements show a slight decrease in CO2 around the 1940s. Analysis with the carbon cycle model and a numerical model of firn processes suggests that about 3 GtC yr-1 uptake (mostly oceanic) is required in the 1940s to match the ice core measurements. The estimates of variation in the terrestrial biospheric flux between 1950 and 1980 from the double deconvolution calculation are in very good agreement with an independent estimate of the global terrestrial flux from a climate-driven ecosystem model.