The Transferable Belief Model is a general framework for managing imprecise and uncertain information using belief functions. In this framework, the discounting operation allows to combine information provided by a source (in the form of a belief function) with metaknowledge regarding the reliability of that source, to compute a “weakened”, less informative belief function. In this article, an extension of the discounting operation is proposed, allowing to make use of more detailed information regarding the reliability of the source in different contexts, a context being defined as a subset of the frame of discernment. Some properties of this contextual discounting operation are studied, and its relationship with classical discounted is explained.