Reliability is a key performance indicator of distributed service systems. On the condition that a customer raises a demand with a very strict reliability, it is possibly difficult for a service broker to offer a composite service that fully satisfies the reliability expectation. In the real world, the customers would like to pay extra money to assure the successful execution of a composite service, and the brokers usually adopt a redundancy-based mechanism to enhance the reliability of the composite service. The authors consider two scenarios of reliability enhancement: (1) a composite service exists but its reliability fails to meet the expectations of customers; and (2) no composite services exist yet, but it is known that the expected reliability is too high to be met. To handle them, the authors propose the RE-ECS and RE-PLN algorithms, respectively, in which three heuristic rules are proposed and the Artificial Bee Colony (ABC) algorithm are adopted to find an approximate optimal trade-off between the improvement extent and the total cost of the reliability enhancement. The authors use two traditional redundancy strategies (i.e., sequential and parallel) for enhancing the reliability a single service task, and a new redundancy strategy called path redundancy for extending a new path into a composite service to improve the global reliability. Nine experiments are conducted and some factors having potential influences on the effect, cost, and efficiency of the reliability enhancement are analyzed. This work is of significance for service brokers to build and enhance their composite services to satisfy those strict expectations on reliability.