Phonological variation is conditioned by both grammatical and non-grammatical factors. Nearly all models of variation in phonological theory are exclusively grammatical, and do not account for the influence of non-grammatical factors at all. In this paper, I argue that an adequate theory of phonological variation should account for both grammatical and non-grammatical influences on variation, and I develop a noisy Harmonic Grammar model of variation that can do this. The constraints used in Harmonic Grammar are ordinary grammatical constraints (as in Optimality Theory), and the influence of grammar on variation follows from this. The influence of non-grammatical factors is accounted for by scaling the weight of faithfulness constraints up or down, resulting in less or more unfaithfulness.