We model an IPO company's optimal response to the presence of sentiment investors and short sale constraints. Given regulatory constraints on price discrimination, the optimal mechanism involves the issuer allocating stock to 'regular' institutional investors for subsequent resale to sentiment investors, at prices the regulars maintain by restricting supply. Because the hot market can end prematurely, carrying IPO stock in inventory is risky, so to break even in expectation regulars require the stock to be underpriced - even in the absence of asymmetric information. However, the offer price still exceeds fundamental value, as it capitalizes the regulars' expected gain from trading with the sentiment investors. This resolves the apparent paradox that issuers, while shrewdly timing their IPOs to take advantage of optimistic valuations, appear not to price their stock very aggressively. The model generates a number of new and refutable empirical predictions regarding the extent of long-run underperformance, offer size, flipping, and lock-ups.