The effects of insulin on the suppression of lipolysis are neither fully understood nor quantified. We examined a variety of mathematical models analogous to the minimal model of glucose disposal (MMG) to quantify the combined influence of insulin on lipolysis and glucose disposal during an insulin-modified frequently sampled intravenous glucose tolerance test. The tested models, which include two previously published ones, consisted of separate compartments for plasma free fatty acids (FFA), glucose and insulin. They differed in the number of compartments and in the action of insulin to suppress lipolysis that decreased the plasma FFA level. In one category of models, a single insulin compartment acted on both glucose and FFA simultaneously. In a second category, there were two insulin compartments, each acting on FFA and glucose independently. For each of these two categories, we tested 11 variations of how insulin suppressed lipolysis. We also tested a model with an additional glucose compartment that acted on FFA. These 23 models were fit to the plasma FFA and glucose concentrations of 102 subjects individually. Using Bayesian model comparison methods, the model that best balanced fit and minimized model complexity was selected. In the best model, insulin suppressed lipolysis via a Hill function through a remote compartment that acted on both glucose and FFA simultaneously and glucose dynamics obeyed the classic MMG.