I report on the results of ongoing language learning experiments with CAMiLLe. CAMiLLe is a computational implementation of a conservative, attentive, minimalist language learner. CAMiLLe has only a very minimal prior knowledge of grammar, forms correspondence rules between sound and meaning, takes account of every bit of linguistic data, and generalizes very conservatively. After a brief description of the architecture of CAMiLLe, I describe how well CAMiLLe performs on a number of grammatical acquisition tasks, such as word order and syntactic correspondences with thematic roles. The tentative conclusion at this point is that CAMiLLe is capable of acquiring a system that is equivalent to the grammar of a human language, although it lacks much of the formal machinery of contemporary grammatical theories.