  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.
