Metrical theory emphasizes rhythmic aspects of stress and treats primary stress as secondary stress plus something extra. This work argues that primary stress in many languages is not governed by rhythm, but is assigned by autonomous principles. An alternative view of primary stress is proposed in which syllables compete for prominence. A small set of constraints account for a wide variety of basic stress patterns and predict the existence of other patterns which are as yet unattested. In detailed analyses of several languages, the new constraints yield insightful accounts of lexically-idiosyncratic stress patterns and of the relationship between stress and morphological structure. The fundamental claims of the model are: (1) primary stress identifies the winner of a competition for prominence; (2) stress systems vary along a continuum defined by the degree to which stress at one edge of a word is favored over stress at the other; (3) stress is affected by the proximity of vowels to the edges of morphological domains; (4) lexically-idiosyncratic stress patterns reflect gradient underlying prominence associated with particular vowels in the lexicon; and (5) the lexicon contains gradient phonological features which function as weighted constraints on surface representations.