In this report, we present a general prescription for computing the escape rate of the system from a basin with full consideration of the topographical fingerprint of that basin. The method is based on a solution of the reduced Fokker-Planck equation and built up to allow the separation of the inter-basin dynamics from that of the intra-basin motion. The main result is that when local well populations thermalize within a basin, local minima, especially those of higher energy, enhance the escape rate from the basin. Also, numerical analyses lead to the inference that kinetic traps of "wrong" structures are distinctive topographical patterns which may produce kinetic properties similar to those of the primary basin, i.e., that containing the global minimum, but lie in other basins.