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We present a new equilibrium search model where consumers initially search among discount opportunities, but are willing to pay more as a deadline approaches, eventually turning to full-price sellers. The model predicts equilibrium price dispersion and rationalizes discount and full-price sellers coexisting without relying on ex ante heterogeneity. We apply the model to online retail sales via auctions and posted prices, where failed attempts to purchase reveal consumers' reservation prices. We find robust evidence supporting the theory. We quantify dynamic search frictions arising from deadlines and show how, with deadline-constrained buyers, seemingly neutral platform fee increases can cause large market shifts.