This paper presents a first attempt at understanding some of the many issues involved in the granting of an amnesty to illegal immigrants. We consider government behavior with respect to allocations on limiting infiltration (border control) and apprehending infiltrators (internal control) and with respect to the granting of amnesties, the timing of amnesties, and limitations on eligibility for those amnesties. We demonstrate the effects of government actions on allocations and the flow of immigrants, and how the interactions between these factors combine to yield an optimal amnesty policy. We also consider various extensions such as intertemporal transfers of policing funds, risk-aversion, and "fuzziness" in declarations regarding eligibility for an amnesty aimed at apprehending and deporting undesirables.