The factors responsible for fast folding and stable 2D lattice proteins are studied by Monte Carlo kinetic simulations and by full enumeration. For weak effective coupling between residues ͑ i.e., high temperatures͒ the folding time is mainly controlled by the free energy gradient. When this coupling is strong, entrapment in local minima plays a major role. The energy gap separating the native state from the remaining conformations shows some correlation to the folding and unfolding times for a

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... variety of sequences. These concepts are related to the ratio T f /T g proposed by Bryngelson and Wolynes. One source of local minima are strong, non-native ͑hindering͒ contacts. An exclusive increase in hindering contacts shows a strong correlation between the energy gap and the folding/unfolding times. Other local minima results from several native contacts that, if formed prematurely, interfere with the formation of others. To study these factors, we use a semispecific model characterized by attractive interactions between similar residues. A procedure to design stabler sequences with smoother landscapes is discussed. By comparing this model to the hydrophobic HP model, we show how higher potential heterogeneity can be used to improve folding.