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This paper presents a novel software pipelining approach, which is called Swing Modulo Scheduling (SMS). It generates schedules that are near optimal in terms of initiation interval, register requirements and stage count. Swing Modulo Scheduling is an heuristic approach that has a low computational cost. The paper describes the technique and evaluates it for the Perfect Club benchmark suite. SMS is compared with other heuristic methods showing that it outperforms them in terms of the quality of the obtained schedules and compilation time. SMS is also compared with an integer linear programming approach that generates optimum schedules but with a huge computational cost, which makes it feasible only for very small loops. For a set of small loops, SMS obtained the optimum initiation interval in all the cases and its schedules required only 5% more registers and a 1% higher stage count than the optimum.