We study folding in 16-monomer heteropolymers on the square lattice. For a given sequence, thermodynamic properties and stability of the native state are unique. However, the kinetics of folding depends on the model of dynamics adopted for the time evolution of the system. We consider three such models : Rouse-Like dynamics with either single monomer moves or with single and double monomer moves, and the "slithering snake＇＇ dynamics. Usually, the snake dynamics has poorer folding properties compared to the Rouse-like dynamics, but examples of opposite behavior can also be found. This behavior relates to which conformations act as local energy minima when their stability is checked against the moves of a particular dynamics. A characteristic temperature related to the combined probability, P-L, to stay in the non-native minima during folding coincides with the temperature of the Fastest folding. Studies of P-L yield an easy numerical way to determine conditions of the optimal folding.