The Diamond paradox says that competing firms offering perfect substitutes set monopoly prices if consumers have strictly positive search costs. By contrast, if consumers are fully informed, with constant marginal costs the perfectly competitive outcome prevails. In our setting, consumers have zero search costs and search sequentially for the best price. At least one firm is capacity-constrained and thus cannot serve all consumers at the competitive price. We provide conditions such that in duopoly, firms set the monopoly price. We provide further equilibrium characterization when these conditions are not satisfied.