The present study explores the role of the word position-in-text in sentence and paragraph reading. Three eye-movement data sets based on the reading of Dutch and German unrelated sentences reveal a sizeable, replicable increase in reading times over several words at the beginning and the end of sentences. The data from the paragraph-based English-language Dundee corpus replicate the pattern and also indicate that the increase in inspection times is driven by the visual boundaries of the text organized in lines, rather than by syntactic sentence boundaries. We argue that this effect is independent of several established lexical, contextual, and oculomotor predictors of eye-movement behaviour. We also provide evidence that the effect of word position-in-text has two independent components: a start-up effect, arguably caused by a strategic oculomotor programme of saccade planning over the line of text, and a wrap-up effect, originating in cognitive processes of comprehension and semantic integration.