Three experiments investigated strategies readers use to process locally ambiguous unbounded dependency constructions. Using self-paced reading, Experiments 1 and 2 manipulated subcategorisation preferences and plausibility, and found that readers initially misanalysed a noun-phrase filler as an object of a verb, whether or not the verb preferentially took a noun-phrase object. Using eye-movement monitoring, Experiment 3 showed that readers misanalysed when the verb preferentially did not take a noun-phrase object in normal reading. These results indicate that readers do not select an initial analysis for an unbounded dependency construction on the basis of subcategorisation frequency. Indeed, the preference for forming such dependencies as quickly as possible does not seem to be affected by the verb’s subcategorisation preferences. We discuss the implications of the results for theories of parsing.