Stochastic modelling and simulation is a well-known approach for predicting the behaviour of biochemical systems. Its main applications lie in those systems wherein the inherently random fluctuations of some species are significant, as often is the case whenever just a few macromolecules have a large effect on the rest of the system. The Gillespie’s stochastic simulation algorithm (SSA) is a standard method to properly realise the stochastic nature of reactions. In this paper we propose an improvement to SSA based on the Huffman tree, a binary tree which is used to define an optimal data compression algorithm. We exploit results from that area to devise an efficient search for next reactions, moving from linear time complexity to logarithmic complexity. We combine this idea with others from literature, and compare the performance of our algorithm with previous ones. Our experiments show that our algorithm is faster, especially on large models.