Mathematically convenient models for a search can be based on a prior representation of the hidden objects and their values by a mixture of Poisson processes. In simple cases, we can find the corresponding Bayes procedures to maximise expected net gains, allowing for the cost of searching. More generally, optimal stopping rules for the search axe difficult to construct and evaluate. We also investigate a procedure based on the asymptotic behaviour of the system when the number of hidden objects is large. This is shown to provide a reasonably effective stopping rule over a wide range of conditions.