Various models have been proposed to quantitate from [18F]-Fluoro-Deoxy-Glucose ([18F]FDG) positron emission tomography (PET) data glucose regional metabolic rate. We evaluate here four models, a three-rate constants (3K) model, a four-rate constants (4K) model, an heterogeneous model (TH) and a spectral analysis (SA) model. The data base consists of [18F]FDG dynamic data obtained in the myocardium and brain gray and white matter. All models were identified by nonlinear weighted least squares with weights chosen optimally. We show that: 1) 3K and 4K models are indistinguishable in terms of parsimony criteria and choice should be made on parameter precision and physiological plausibility; in the gray matter a more complex model than the 3K one is resolvable; 2) the TH model is resolvable in the gray but not in the white matter; 3) the classic SA approach has some unnecessary hypotheses built in and can be in principle misleading; we propose here a new SA model which is more theoretically sound; 4) this new SA approach supports the use of a 3K model in the heart with a 60 min experimental period; it also indicates that heterogeneity in the brain is modest in the white matter; 5) [18F]FDG fractional uptake estimates of the four models are very close in the heart, but not in the brain; 6) a higher than 60 min experimental time is preferable for brain studies.