An eye-tracking experiment in Danish investigates two dominant accounts of sentence processing: locality-based theories that predict a processing advantage for sentences where the distance between the major syntactic heads is minimized, and the surprisal theory which predicts that processing time increases with big changes in the relative entropy of possible parses, sometimes leading to anti-locality effects. We consider both lexicalised surprisal, expressed in conditional trigram probabilities, and syntactic surprisal expressed in the manipulation of the expectedness of the second NP in Danish constructions with two postverbal NP-objects. An eye-tracking experiment showed a clear advantage for local syntactic relations, with only a marginal effect of lexicalised surprisal and no effect of syntactic surprisal. We conclude that surprisal has a relatively marginal effect, which may be clearest for verbs in verb-final languages, while locality is a robust predictor of sentence processing.