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Heterogeneous soft multiprocessor systems are likely to find a larger share in the application-specific computing market due to increasing cost and defect rates in foreseeable manufacturing technologies. We study the problem of mapping streaming applications onto heterogeneous soft dual-processor systems, in which processors' limited memory resources and application throughput form the outstanding constraints and objective, respectively. A key step in the compilation process is task assignment, where tasks are assigned to the processors. We develop a provably-effective algorithm for task assignment. Our algorithm is versatile, in that its formal properties hold for, and hence it is applicable to, a variety of platforms. Measurement of generated code size, and throughput of emulated systems validate the effectiveness of our approach. We advance the state-of-the-art by considerably outperforming two recent competitors in terms of both versatility and application throughput.