To acquire one's native phonological system, language-specific phonological categories and relationships must be extracted from the input. The acquisition of the categories and relationships has each in its own right been the focus of intense research. However, it is remarkable that research on the acquisition of categories and the relations between them has proceeded, for the most part, independently of one another. We argue that this has led to the implicit view that phonological acquisition is a "two-stage" process: Phonetic categories are first acquired and then subsequently mapped onto abstract phoneme categories. We present simulations that suggest two problems with this view: First, the learner might mistake the phoneme-level categories for phonetic-level categories and thus be unable to learn the relationships between phonetic-level categories; on the other hand, the learner might construct inaccurate phonetic-level representations that prevent it from finding regular relations among them. We suggest an alternative conception of the phonological acquisition problem that sidesteps this apparent inevitability and acquires phonemic categories in a single stage. Using acoustic data from Inuktitut, we show that this model reliably converges on a set of phoneme-level categories and phonetic-level relations among subcategories, without making use of a lexicon. (Contains 4 figures, 4 tables, and 2 notes.)