We studied several group testing models with and without processing times. The objective was to choose an optimal group size for pooled screening of a contaminated population so as to collect a prespecified number of good items from it with minimum testing expenditures. The tested groups that were found to be contaminated were used as a new sampling population in later stages of the procedures. Since testing may be time-consuming, we also considered deadlines to be met for the testing process. We derived algorithms and exact results for the underlying distributions, enabling us to find optimal procedures. Several numerical examples are given.