This essay is about bribe chains in police departments. A chain starts with an apprehended offender paying a bribe to a policeman.1 If the policeman is caught, in turn, by a superior officer, he pays a bribe to get the collusion and the offence ignored. It is alleged that bribes from original offenders thus pass upwards to the top through intervening levels. Frequent occurrence of offences and bribing help form a steady pattern of sharing of the spoils among various levels of the administration. We will model such a chain and then use it to explore administrative structures that can deter them.