It has been proposed that language processing invokes extra-grammatical heuristics in addition to, or instead of the computational system (e.g., Townsend & Bever, 2001; Karimi & Ferreira, 2016). The outputs of these extra-grammatical heuristics are called “good-enough” representations. These representations lack (syntactic) detail and are incomplete (Karimi & Ferreira, 2016). This paper evaluates this claim by investigating one extra-grammatical processing heuristic in particular: the NV(N)-strategy. Two experiments prove that (i) interpretations that would result from application of the NV(N)-strategy are sometimes difficult to generate and (ii) listeners compute (syntactic) representations for sentences that are more detailed than the NV(N)-strategy would predict. This gives rise to the question whether “good-enough” representations are computed at all.