This dissertation investigates the Complement Problem, which second language learners face when the set of forms grammatical in their second language (L2) is a subset of those grammatical in their first language (L1). This problem arises due to two common assumptions: (1) the Subset Principle, and (2) full transfer of L1 properties to the L2 grammar. According to the Subset Principle, learning follows a path from the most restrictive grammar to less restrictive grammars. If L1 properties are fully transferred to the L2, then this in combination with the Subset Principle creates the Complement Problem: a learner begins with the L1 grammar and then needs to move into a more restrictive grammar. If both (1) and (2) hold, the L2 learner is expected to never be able to learn that some of the forms grammatical in their L1 are ungrammatical in their L2. I present experimental evidence that shows that learners are able to acquire this knowledge. L2 learners of English and Spanish participated in wordlikeness rating tasks and direct comparisons of different forms, both of which illustrated the successful acquisition of ungrammatical forms in the L2. In a set of experiments focused on final consonants in English and Spanish, L1 EnglishL̃2 Spanish speakers exhibited knowledge in Spanish of the ungrammaticality of some final consonants, even when those final consonants were legal in English. A second set of experiments showed similar results for L1 SpanishL̃2 English speakers' judgments of consonantg̃lideṽowel sequences in Spanish and English. These results indicate that the acquisition of ungrammaticality is possible in L2 learning. In order to account for this knowledge, I propose a modification to Escudero's (2005) Second Language Linguistic Perception Model in which the L2 grammar is not fully transferred. Instead, the perception grammar reverts to the most restrictive state, while the production grammar is fully transferred to the L2. This modification, which I call Perceptual Full Access, accounts for the subset knowledge seen in the experiments presented here, as well as continuing to account for transfer effects in both production and perception, as it was designed to do