A model is proposed using the run-off triangle of paid claims and also the numbers of reported claims (in a similar triangular array). These data are usually available, and allow the model proposed to be implemented in a large variety of situations. On the basis of these data, the stochastic model is built from detailed assumptions for individual claims, but then approximated using a compound Poisson framework. The model explicitly takes into account the delay from when a claim is incurred and to when it is reported (the IBNR delay) and the delay from when a claim is reported and to when it is fully paid (the RBNS delay). These two separate sources of delay are estimated separately, unlike most other reserving methods. The results are compared with those of the chain ladder technique.