Cyclic pursuit is a simple distributed control law in which agent i pursues agent i + 1 modulo n. We generalize existing results and show that by selecting the gains of the agents, the point of convergence of these agents can be controlled. The condition for convergence, the range of controller gains and the reachable set where convergence can occur are studied. It is also shown that the sequence in which an agent pursues another does not affect the point of convergence.