Estimating parameters in biochemical network models is a central but often difficult problem. A general approach that may be worth developing further is first to seek simplified or "reduced" models with fewer dynamical degrees of freedom, estimate parameters for the reduced models, and then use that information to constrain the corresponding parameters in the full model. This approach can leverage appropriate human expertise and could in principle be applied recursively. The choice of variables to eliminate during model reduction could also be made by clustering or other machine learning methods. Some relevant model reductions already exist for quasi-equilibrium models of transcriptional regulation networks, which could provide a starting point for this strategy.