How should a firm with limited capacity introduce a new product? Should it introduce the product as soon as possible or delay introduction to build up inventory? How do the product and market characteristics affect the firm's decisions? To answer such questions, we analyze new product introductions under capacity restrictions using a two-period model with diffusion-type demand. Combining marketing and operations management decisions in a stylized model, we optimize the production and sales plans of the firm for a single product. We identify four different introduction policies and show that when the holding cost is low and the capacity is low to moderate, a (partial) build-up policy is indeed optimal if consumers are sensitive to delay. Under such a policy, the firm (partially) delays the introduction of its product and incurs short-term backlog costs to manage its future demand and total costs more effectively. However, as either the holding cost or the capacity increases, or consumer sensitivity to delay decreases, the build-up policy starts to lose its appeal, and instead, the firm prefers an immediate product introduction. We extend our analysis by studying the optimal capacity decision of the firm and show that capacity shortages may be intentional.