Two sequential procedures (one based on an initial group test) for reducing exposure to personnel leak-testing sealed radium sources where it is assumed that exposure is directly proportional to the activity of the source(s) being tested, were proposed in [19]. These procedures, based on finding at most one leaker, were evaluated and compared using a conditional binomial model—ne that assumed the presence of at most one leaker in the group being tested. Here the evaluation and comparison of the two procedures are based on a more realistic unconditional binomial model; in addition these two procedures are generalized to the case where at mostDleakers are searched for. The results obtained using both the conditional and unconditional models are compared.