This paper presents a combination of synthesis inversion and simulated annealing as a method for suggesting optimal networks for constraining the global carbon budget. Synthesis inversion uses an atmospheric tracer transport model and, in our applications, prior estimates of sources to return estimates of sources' strengths along with their uncertainties. Simulated annealing is a commonly used technique for optimizing multi-variate functionals. By treating the predicted uncertainty for a source as this functional and station locations as parameters, we are able to suggest improved observing networks. The results suggest that considerable improvement is possible with current station densities. Further, they suggest surprising constraints are possible because of the combination of apparently disparate data by the inversion technique. For example, the best improvement available in estimates of total ocean uptake from one extra station is obtained when that station is sited over tropical South America. This follows from the global balances of the CO2 budget. Finally, considerable specificity is required in defining the objectives for such an optimization, since apparently similar quantities might require very different strategies.