This paper reports results from a series of laboratory experiments designed to evaluate the impact of exposure risk on market performance. Exposure risk arises when there are complementarities between trades, e.g. when the purchase of a new house requires selling the old one. The continuous double auction (CDA), which has proven to be remarkably effective in a wide variety of settings, performs poorly in a treatment with high exposure risk: overall market efficiency is only 20% and there are many instances of no trade. In a parallel treatment with lower exposure risk, efficiency under the CDA is higher (55%) but is dominated, for instance, by a top-trading-cycles procedure that uses no money. The CDA's poor performance does not depend on whether house values are private information or common knowledge, indicating that exposure risk is due to strategic uncertainty not objective uncertainty about others' preferences. We introduce a simple package market and show that it effectively resolves exposure risk: efficiency levels are 82% and 89% respectively for the low and high exposure treatments. The proposed package market is a simple extension of the CDA and could potentially be applied in a variety contexts.