This study evaluates a recent account of islands and parasitic gaps, which proposes that island violations are unacceptable in part because they contain a referring argument in the predicate that contributes discourse-processing complexity. In two acceptability judgment experiments in Dutch, participants rated three types of filler-gap constructions that were preceded by a context manipulating the discourse accessibility of a referring argument in the target construction. The constructions differed in the location of the gap, which was realized as the complement of the matrix verb (regular filler-gap dependencies), as the complement of the verb in an adjunct clause (adjunct island violations), or as both (parasitic gap constructions). Adjunct clauses were untensed in Experiment 1 and tensed in Experiment 2. In both experiments, island violations were rated as unacceptable, regardless of whether the referring argument was discourse-accessible or discourse-novel. Parasitic gap constructions, which do not contain a referring argument in the predicate, were rated as acceptable, but only when the parasitic gap was located in an untensed clause. Reviewing these results from syntactic and discourse-processing perspectives, we conclude that the difference between islands and parasitic gap constructions is not a matter of discourse-processing complexity. The data instead support a primarily syntactic account of parasitic gaps.