We investigate an IPO security design problem when information asymmetries across investors lead to a winner’s curse. Firms that are riskier in down markets can lower the cost of going public by using unit IPOs, in which equity and warrants are combined into a non-divisible package. Furthermore, firms that have a sizeable growth potential even in bad states of the world can fully eliminate the winner’s curse problem by making the warrants callable. Our theory is consistent with the prominent use of unit IPOs and produces empirical implications that differentiate it from existing theories.