When combining information across different senses humans need to flexibly select cues of a common origin whilst avoiding distraction from irrelevant inputs. The brain could solve this challenge using a hierarchical principle, by deriving rapidly a fused sensory estimate for computational expediency and, later and if required, filtering out irrelevant signals based on the inferred sensory cause(s). Analysing time- and source- resolved human magnetoencephalographic data we unveil a systematic ...