Due to its complexity, the problem of mapping and scheduling streaming applications on heterogeneous MPSoCs under real-time and performance constraints has traditionally been tackled by incomplete heuristic algorithms. In recent years, approaches based on Constraint Programming (CP) have shown promising results as complete methods for finding optimal mappings, in particular concerning throughput. However, so far none of the available CP approaches consider the tradeoff between throughput and buffer requirements or throughput and power consumption. This article integrates tradeoff awareness into the CP model and introduces a two-step solving approach that utilizes the advantages of heuristics, while still keeping the completeness property of CP. With a number of experiments considering several streaming applications and different platform models, the article illustrates not only the efficiency of the presented model but also its suitability for solving different problems with various combinations of performance constraints.