While maximum standard absolute adjectives (such as straight) typically have a precise meaning (e.g., ‘perfectly straight’), they are also regularly used imprecisely (e.g., to mean ‘straight enough’). The current study investigates how contextual expectations of precision and a visual referent’s conceptual distance from an ideal maximum standard influence the processing effort of precise and imprecise interpretations of these adjectives. In three experiments, we showed native speakers of English images depicting objects that could be referred to precisely or imprecisely via an absolute adjective and asked them to select the image that best matched the written sentence (Experiments 1 and 2) or to read sentences containing maximum standard absolute adjectives (Experiment 3). Experiment 1 presented no discourse context, and participants accepted, on average, only a small degree of imprecision; and when they did, they took longer, relative to cases in which the same adjectives were used precisely, which is in line with existing empirical findings. Experiment 2 contrasted two kinds of discourse contexts (raising high or low expectations of precision) before the presentation of the test sentences. When expectations of precision were high, participants tolerated only a small degree of imprecision, and when they did, it came at a cost, as in Experiment 1. When expectations of precision were low, much larger degrees of imprecision were tolerated but, critically, participants were still, overall, faster to reach precise, relative to imprecise, interpretations in supporting contexts, suggesting that accessing the precise meaning is less effortful. Experiment 3 supported these findings by showing how the cost of understanding imprecision is also present in a self-paced reading task. Our results lend support to the view that maximum standards are part of the encoded meaning of these adjectives.