In this paper, we report two experiments in Spanish designed to find out what kind of processes underlie the online parsing of complex noun phrases (NPs). To that end, we used a ‘click detection’ paradigm coupled with an oral comprehension task with sentences made up of complex NPs comprising embedded prepositional phrases PPs or coordinate NPs. The critical NPs consisted of words or pseudowords, and were inserted either at subject position (Experiment 1) or at object position (Experiment 2) in the sentence. Results show an opposite pattern of RTs to clicks when the complex NP is located at subject (vs. object) position, with the former case showing heavier processing demands as the parser delves deeper into the complex NP, regardless of the internal constituency of the target NP and its lexical content, and the latter yielding the opposite pattern. These results suggest that structural complexity by itself does not determine an increase in processing costs during sentence parsing, which is only apparent in cases involving deferred operations like subject-verb agreement.