We model a simple market setting in which fragmentation of trade of the same asset across multiple exchanges improves allocative effciency. Fragmentation reduces the inhibiting effect of price-impact avoidance on order submission. Although fragmentation reduces market depth on each exchange, it also isolates cross-exchange price impacts, leading to more aggressive overall order submission and better rebalancing of unwanted positions across traders. Fragmentation also has implications for the extent to which prices reveal traders' private information. While a given exchange price is less informative in more fragmented markets, all exchange prices taken together are more informative.