Within systems biology there is an increasing interest in the stochastic behaviour of biochemical reaction networks. An appropriate stochastic description is provided by the chemical master equation, which represents a continuous-time Markov chain (CTMC). The uniformisation technique is an efficient method to compute probability distributions of a CTMC if the number of states is manageable. However, the size of a CTMC that represents a biochemical reaction network is usually far beyond what is feasible. In this study, the authors present an on-the-fly variant of uniformisation, where they improve the original algorithm at the cost of a small approximation error. By means of several examples, the authors show that their approach is particularly well-suited for biochemical reaction networks.