Environmental engineering decisions are often made with limited information. In such cases it is useful to express uncertain quantities with a probability distribution. The use of information theory to estimate probability distributions, given limited information, is illustrated in this paper. Such distributions are as 'broad' as possible consistent with available information, and therefore represent what is known in an objective way. The distributions can be used directly to aid decision-making or as input to stochastic computer models. The estimation of the distribution of particle sizes in a filter media using information theory is demonstrated.