Simulations by isothermal and isoergic molecular dynamics show that vibrationally-cold clusters, initially at some high-energy point on their potential surfaces, relax monotonically down to low-lying minima where they are trapped. The most significant point regarding this relaxation is that species with sawtoothlike and staircaselike potentials show the same qualitative behavior, equilibrating their vibrations after each major saddle crossing. This result justifies the use of transition state kinetics for constructing coarse-grained master equations to describe the well-to-well flow of population distributions on complex potential energy surfaces, even in cases such as (KCl)(32) and some protein models which have staircase topographies in which large drops in potential energy from one well to the next might suggest nonthermal kinetics could occur.