It is commonly assumed that innate linguistic constraints are necessary to learn a natural language, based on the apparent lack of explicit negative evidence provided to children and on Gold's proof that, under assumptions of virtually arbitrary positive presentation, most interesting classes of languages are not learnable. However, Gold's results do not apply under the rather common assumption that language presentation may be modeled as a stochastic process. Indeed, Elman (Elman, J.L., 1993. Learning and development in neural networks: the importance of starting small. Cognition 48, 71-99) demonstrated that a simple recurrent connectionist network could learn an artificial grammar with some of the complexities of English, including embedded clauses, based on performing a word prediction task within a stochastic environment. However, the network was successful only when either embedded sentences were initially withheld and only later introduced gradually, or when the network itself was given initially limited memory which only gradually improved. This finding has been taken as support for Newport's 'less is more' proposal, that child language acquisition may be aided rather than hindered by limited cognitive resources. The current article reports on connectionist simulations which indicate, to the contrary, that starting with simplified inputs or limited memory is not necessary in training recurrent networks to learn pseudonatural languages; in fact, such restrictions hinder acquisition as the languages are made more English-like by the introduction of semantic as well as syntactic constraints. We suggest that, under a statistical model of the language environment, Gold's theorem and the possible lack of explicit negative evidence do not implicate innate, linguistic-specific mechanisms. Furthermore, our simulations indicate that special teaching methods or maturational constraints may be unnecessary in learning the structure of natural language.