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Failure semantics in communication models for distributed systems deal with the impossibility of achieving an exactly once invocation semantics in failure-prone environments. For remote procedure invocation models, failure semantics such as at-least-once and at-most-once specify guarantees about the number of executions of an invocation as well as its completeness even under the assumption that communication and server failures may occur. While such failure semantics are quite successful for remote procedure call models they have significant weaknesses when applied to streaming media communication. The main reasons are fundamental differences in the basic communication model as well as case-dependency and granularity of failure treatment in media streams, resulting in awkward abstractions as well as inefficient implementations. This paper is a step towards an adaptive failure semantics for streaming media communication. We argue that in order to achieve simplicity and economy, failure semantics must dynamically exploit application-level knowledge as well as knowledge from lower system layers, the three corner stones being media stream structure, timing constraints and resource availability. The paper focuses on structure-awareness as one of these three corner stones. It discusses the role of importance of a media stream fragment, develops a function to quantify importance, and discusses its computability. Experimental results evaluating importance based failure handling conclude the work.