{This paper addresses the problem of simplifying chemical reaction networks by adroitly reducing the number of reaction channels and chemical species. The analysis adopts a discrete-stochastic point of view and focuses on the model reaction set S-1 -><- S-2 -> S-3, whose simplicity allows all the mathematics to be done exactly. The advantages and disadvantages of replacing this reaction set with a single S-3-producing reaction are analyzed quantitatively using novel criteria for measuring simulation accuracy and simulation efficiency. It is shown that in all cases in which such a model reduction can be accomplished accurately and with a significant gain in simulation efficiency, a procedure called the slow-scale stochastic simulation algorithm provides a robust and theoretically transparent way of implementing the reduction.}