We discuss fine-tuning constraints on supergravity models. The tightest constraints come from the experimental mass limits on two key particles: the lightest CP even Higgs boson and the gluino. We also include the lightest chargino which is relevant when universal gaugino masses are assumed. For each of these particles we show how fine-tuning increases with the experimental mass limit, for four types of supergravity model: minimal supergravity, no-scale supergravity (relaxing the universal gaugino mass assumption), D-brane models and anomaly mediated supersymmetry breaking models. Among these models, the D-brane model is less fine tuned.The experimental propects for an early discovery of Higgs and supersymmetry at LEP and the Tevatron are discussed in this framework.

17 pages, Latex, including 5 eps figures