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Service-Oriented Architecture enables the composition of loosely coupled services provided with varying Quality of Service (QoS) levels. Given a composition, finding the set of services that optimizes some QoS attributes under given QoS constraints has been shown to be NP-hard. Therefore, heuristic algorithms are widely used, finding acceptable solutions in polynomial time. Still the time complexity of such algorithms can be prohibitive for real-time use, especially if the algorithms are required to run until they find near-optimal solutions. Thus, we propose a heuristic approach based on Hill-Climbing that makes effective use of an initial bias computed with Linear Programming, and works on a reduced search space. In our evaluation, we show that our approach finds near-optimal solutions and achieves a low time complexity.