A force of mobile targets is subject to a long period of surveillance, followed by a sudden application of force (the 'pounce'). Some targets will escape the pounce because they have not been recently enough localized by the surveillance system. The problems considered are the division of a budget between surveillance and pounce, the allocation of pounce forces to targets, and the description of how the fraction of targets that survives the pounce depends on the budget. (Author)