We investigate how not-at-issue content is integrated into a sentence by comparing the online attachment of parenthetical relative clauses to that of better-studied restrictive relative clauses. In an eye-tracking experiment, we report an early penalty for high attachment in restrictive relative clauses (as predicted by processing principles such as late closure or recency) but not for parenthetical relative clauses. These findings suggest that the processor delays structural integration of not-at-issue material, even when attachment is disambiguated by verb agreement. A preliminary or underspecified parse may initially be computed for parenthetical clauses during comprehension.