We apply to Classical Labrador Sea Water (CLSW) the transit-time distribution (TTD) method to estimate the inventory and uptake of anthropogenic carbon dioxide (Cant). A model of TTDs representing bulk-advection and diffusive mixing is constrained with CFC11 data. The constrained TTDs are used to propagate Cant into CLSW, allowing the air-sea disequilibrium to evolve consistently. Cant in the Labrador Sea (LS) surface waters cannot keep pace with increasing atmospheric CO2 and is highly undersaturated. Our best estimate for 2001 is an anthropogenic inventory of 1.0 Gt C and an uptake of 0.02 Gt C/year. By additionally using the constraint of present-day CO2 measurements, we estimate that the preindustrial LS was neutral or a weak source of CO2 to the atmosphere. Our estimates are subject to possible error due to the assumption of steady-state transport and carbon biochemistry.