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Enhanced pipeline scheduling (EPS) is a software pipelining technique which can achieve a variable initiation interval (II) for loops with control flows via its code motion pipelining. EPS, however, leaves behind many renaming copy instructions that cannot be coalesced due to interferences. These copies take resources, and more seriously, they may cause a stall if they rename a multi-latency instruction whose latency is longer than the II aimed for by EPS. This paper describes how those renaming copies can be deleted through unrolling, which enables EPS to avoid a serious slowdown from latency handling and resource pressure while keeping its variable II and other advantages. In fact, EPS's renaming through copies, followed by unrollbased copy elimination, provides a more general and simpler solution to the cross-iteration register overwrite problem in software pipelining which works for loops with control flows as well as for straight-line loops. Our empirical study performed on a VLIW testbed with a two-cycle load latency shows that the unrolled version of the 16-ALU VLIW code includes fewer no-op VLIWs caused by stalls, improving the performance by a geometric mean of 18%, yet the peak improvement with a longer latency reaches as much as a geometric mean of 25%.