Estimating CO2 fluxes from the pattern of atmospheric CO2 concentrations with atmospheric transport models is an ill-posed inverse problem, whose solution is stabilized using prior information. Weights assigned to prior information and to CO2 concentrations at different locations are quantified by parameters that are not well known, and differences in the choice of these parameters contribute to differences among published estimates of the regional partitioning of CO2 fluxes. Following the TransCom 3 protocol to estimate CO2 fluxes for 1992--1996, we find that the partitioning of the CO2 sink between land and oceans and between North America and Eurasia depends on parameters that quantify the relative weight given to prior flux estimates and the extent to which CO2 concentrations at different stations are differentially weighted. Parameter values that minimize an estimated prediction error can be chosen by generalized cross-validation (GCV). The GCV parameter values yield fluxes in northern regions similar to those obtained with the TransCom parameter values, but the GCV fluxes are smaller in the poorly constrained equatorial and southern regions.