It is well understood that energy rich polyatomic molecules do not dissociate promptly because the number, P, of their energy states far exceeds the number, N, of the decay channels. In the simplest RRK theory, the fraction N/P is the probability of dissociation. We discuss the distribution of the decay rates of maximal entropy and conclude that it is governed by at most N linearly independent constraints, N < P, or, more typically, N << P. This mathematical requirement already severely restricts the number of constraints. Beyond it however, on physical grounds, one constraint, or at most a few, may be dominant. We discuss why just one constraint, or a few but less than N, can be sufficient to describe the product state distribution.