In this paper, we present a procedure for finding the best LFT uncertainty model by minimizing the ℌ -infinity norm of the uncertainty set with respect to a nominal model subject to known input-output data. The main problem is how to express the data-matching constraints for convenient use in the optimization problem. For some uncertainty structures, they can readily be formulated as a set of linear matrix inequalities (LMIs), for some other structures, LMIs are obtained after certain transformations. There are also cases, when the constraints result in bilinear matrix inequalities (BMIs), which can be linearized to enable an efficient iterative solution. Essentially all LFT uncertainty structures are considered. An application to distillation modeling is included.