This talk briefly reviews flux inversion methods which explicitly include process models for fluxes within their solution method. These so-called data assimilation methods generally reduce the dimensionality of their solution space and include explicit flux models. The talk points out that these methods represent a different form of prior information than the standard background covariances but can be similarly assessed and tested. It also suggests the use of decision theory as a method for choosing whether the smaller uncertainty associated with these methods is worth the increased risk of incorrect solutions. It reaches the tentative conclusion that, with the current state of process models, the highly prescriptive biosphere models used in systems like CCDAS are probably too high risk while the  less strongly parameterised models of fossil fuel systems like FFDAS are more likely to be useful.