In communication, information, and other industries, three-part tariffs are increasingly popular. A three-part tariff is defined by an access price, an allowance, and a marginal price for any usage in excess of the allowance. Empirical nonlinear pricing studies have focused on consumer choice under two-part tariffs. We show that consumer behavior differs under three-part tariffs and assess how consumer demand uncertainty impacts tariff choice. We develop a discrete/continuous model of choice among three-part tariffs and estimate it using consumer-level data on Internet usage. Our model extends prior work in accommodating consumer switching to competitors, thereby capturing behavior in competitive industries more accurately. Our empirical work shows that demand uncertainty is a key driver of choice among three-part tariffs. Consumers' expected bill increases with the variation in their usage, steering them toward tariffs with high allowances. Consequently, demand uncertainty decreases consumer surplus and increases provider revenue. A further analysis of consumers' responsiveness to the different elements of a three-part tariff under the provider's current pricing structure reveals that prices affect a consumer's tariff choice more than her usage quantity and that the allowance plays a strong role in consumer tariff choice. Based on our results, we derive implications for pricing with three-part tariffs.