This article contributes to the study of approximative adverbs almost and barely by providing psycholinguistic evidence for the asymmetry of their meaning components. The experiments reported are discussed against the background of a set of tests targeting the theoretical status of the meaning components. The first experiment addresses the role played by each meaning component in textual coherence, whereas the second experiment addresses the interpretation in isolation of a sentence containing an approximative adverb. The results argue for a pragmatic difference in the role of the meaning components, along the lines of Horn's (Assertoric inertia and NPI licensing: 55–82, 2002) proposal, pertaining to the way in which the implications of approximative adverbs contribute to context update.