The efficient processing of sentences in native speakers is the result of great automaticity and speed both in lexical retrieval and in structural computations. In lexical retrieval, all interpretations of a word are accessed, and non-convergent interpretations are quickly pruned. Garden paths also suggest the autonomy of syntactic computations from contextual knowledge, although there is semantic feedback on proposed syntactic attachments at every stage of processing. Early effects of both lexical and contextual semantic knowledge also point to immediate discourse-semantics processing. Sentence processing, therefore, involves computations in various sub-modules, in the limits of their interfaces (Crocker, 1996; inter alia). Sentence processing includes structural computations that are blind to other sources of knowledge. This blindness is a presumed source of efficiency. However, this efficiency comes at the price of a certain dumbness as the processor seems to be unable to learn from its mistakes, taking the same routes over and over even if they are dead-ends leading to garden paths (Fodor, 1983, 2000). Grammatical research argues that a generative computational system specialized for human language (CHL) plays a significant role in giving language its expressive power. CHL crucially mediates between lexical information and the conceptual intentional system (CI-system) that interfaces with CHL at the level of Logical Form (LF). Thus, constraints on movements and on binding appear to be specific to natural-language grammars. Indeed, formal logical systems do not have such constraints. Grammatical research in the generative paradigm has attempted to understand the role of CHL, with all its idiosyncrasies, in language design in terms of mental constitution. Hence, research on the grammar of anaphora (Reuland, 2001; Reinhart & Reuland, 1993) and research on the processing of movement dependencies (Gibson, 1998, 2000; Gibson & Warren, 2004) both conclude that the computation of referential dependencies in syntax plays a central role in the management of the global processing load. Binding reduces the number of assignments of values to variables (Reuland, 2001; Reinhart & Reuland, 1993) and movement traces refresh the activation of referents in discourse-semantics (Gibson, 1998, 2000; Gibson & Warren, 2004). Quirky grammatical dependencies are pervasive in human languages and their target-like acquisition is not trivial for the second language (L2) learner. Formal grammatical rules constitute a non-negligible portion of what needs to be acquired, in addition to vocabulary items. Beyond either the perceived or real needs of L2 learners to approximate the target-language norms or their personal desire to do so, one may wonder whether there are any benefits to formal grammatical rules in L2 acquisition. CHL computations of grammatical rules clearly involve costs, but the dependencies that these computations establish might also eke out efficiencies in the CI-system in return. Benefits to discourse-semantics processing, if they can be found, could offer insights into the role of UGconstrained grammatical states in L2 cognition. Given that a range of cognitive abilities are available