Despite all the progress in Web service selection, the need for an approach with a better optimality and performance still remains. This paper presents a genetic algorithm by adopting the Pareto principle that is called GAP2WSS for selecting a Web service for each task of a composite Web service from a pool of candidate Web services. In contrast to the existing approaches, all global QoS constraints, interservice constraints, and transactional constraints are considered simultaneously. At first, all candidate Web services are scored and ranked per each task using the proposed mechanism. Then, the top 20 percent of the candidate Web services of each task are considered as the candidate Web services of the corresponding task to reduce the problem search space. Finally, the Web service selection problem is solved by focusing only on these 20 percent candidate Web services of each task using a genetic algorithm. Empirical studies demonstrate this approach leads to a higher efficiency and efficacy as compared with the case that all the candidate Web services are considered in solving the problem.