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A review of international terrorist activity reveals a pattern of financially strapped operatives working for organizations that seem to have plenty of money. To explain this observation, and to examine when restricting terrorists' funds will reduce their lethality, we model a hierarchical terror organization in which leaders delegate financial and logistical tasks to middlemen, but cannot perfectly monitor them for security reasons. These middlemen do not always share their leaders' interests: the temptation exists to skim funds from financial transactions. When middlemen are sufficiently greedy and organizations suffer from sufficiently strong budget constraints, leaders will not fund attacks because the costs of skimming are too great. Using general functional forms, we find important nonlinearities in terrorists' responses to government counter-terrorism. Restricting terrorists' funds may be ineffective until a critical threshold is reached, at which point cooperation within terrorist organizations begins to break down and further government actions have a disproportionately large impact.