High-speed market connections improve investors' ability to search for attractive quotes in fragmented markets, raising gains from trade. They also enable fast traders to observe market information before slow traders, generating adverse selection, and thus negative externalities. When investing in fast trading technologies, institutions do not internalize these externalities. Accordingly, they overinvest in equilibrium. Completely banning fast trading is dominated by offering two types of markets: one accepting fast traders, the other banning them. However, utilitarian welfare is maximized by having i) a single market type on which fast and slow traders coexist and ii) Pigovian taxes on investment in the fast trading technology.