Energy distribution functions for the products in two classes of three-atom unimolecular reactions performed in beam experiments are derived which are much more realistic than the prior distribution functions (PDF) of Levine and Bernstein without being more complicated, In a first step, we deal with light-atom emission processes governed by short-range forces. Contrary to what is generally believed, we emphasize the applicability of statistical theory of energy distributions to such reactions in which the change in energy partitioning from critical configuration to products is weak If not negligible. In a second step, we treat within the framework of phase space theory (PST) this more usual case of processes governed by long-range farces for which, however, there exists no realistic distribution functions. Comparison with experimental results or with results of simulations and/or results obtained using PDF, PST, or the statistical adiabatic channel model (SACM) is done for the following processes: (i) C2H --> C-2 + H (model alkyl dissociation reaction), (ii) O3H --> O-2 + H, (iii) NO2 --> NO + O, and (iv) Al-3 --> Al-2 + Al. For reaction i which proceeds through a barrier and for reaction ii which is barrierless but involves strong angular anisotropies in the exit-channel part of the potential energy surface, the distributions derived by our method are much more realistic than those obtained using BST or SACM.