One-to-one promotions are possible when consumers are individually addressable and firms know something about each customer's preferences. We explore the competitive effects of one-to-one promotions in a model with two competing firms where the firms differ in size and consumers have heterogeneous brand loyalty. We find that one-to-one promotions always lead to an increase in price competition (average prices in the market decrease). However, we also find that one-to-one promotions affect market shares. This market-share effect may outweigh the effect of lower prices, benefiting the firm whose market share increases. Our results suggest that of two firms, the firm with the higher-quality product may gain from one-to-one promotions. Our model also has implications for the phenomenon of customer churn, where consumers switch to a less preferred brand due to targeted promotional incentives. We show that churning can arise optimally from firms pursuing a profit-maximizing strategy. Instead of trying to minimize it, the optimal way to manage customer churn is to engage in both offensive and defensive promotions with the relative mix depending on the marginal cost of targeting.