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Complex media fusion operations can be costly in terms of the time they need to process input objects. If data arrive faster to fusion nodes than the speed with which they can consume the inputs, this will result in some input objects not being processed. In this paper, we develop load shedding mechanisms which take into consideration both data quality and expensive nature of media fusion operators. In particular, we present quality assessment models for objects and multistream fusion operators and highlight that such quality assessments may impose partial orders on objects. We highlight that the most effective load control approach for fusion operators involves shedding of (not the individual input objects but) combinations of objects. Yet, identifying suitable combinations of objects in real time will not be possible if efficient combination selection algorithms do not exist. We develop efficient combination selection schemes for scenarios with different quality assessment and target characteristics. We first develop efficient combination-based load shedding when the fusion operator has unambiguously monotone semantics. We then extend this to the more general ambiguously monotone case and present experimental results that show the performance gains using quality-aware combination-based load shedding strategies under the various fusion scenarios.