The conventional approach to calibration global carbon cycle models using 14C from nuclear weapons tests is known to be equivalent to a chain of poorly conditioned deconvolutions. A simple approximate model, relating excess 14C from nuclear testing and anthropogenic CO2 in the atmosphere and ocean surface layer, is used to explore the calibration problem in more detail. Analysis of this model reveals that the calibration is particularly sensitive to the time response describing the uptake of excess 14C by the terrestrial biota.