To achieve high resource utilization for multi-issue Digital Signal Processors (DSPs), production compilers commonly include variants of the iterative modulo scheduling algorithm. However, excessive cyclic data dependences, which exist in communication and media processing loops, often prevent the modulo scheduler from achieving ideal loop initiation intervals. As a result, replicated functional units in multi-issue DSPs are frequently underutilized. In response to this resource underutilization problem, this paper describes a compiler preprocessing strategy that capitalizes on two techniques for effective modulo scheduling, referred to as cloning1 and cloning2. The core of the proposed techniques lies in the direct relaxation of cyclic data dependences by exploiting functional units which are otherwise left unused. Since our preprocessing strategy requires neither code duplication nor additional hardware support, it is relatively easy to implement in DSP compilers. The strategy proposed has been validated by an implementation for a StarCore SC140 optimizing C compiler.