Tying contracts can prevent unravelling in markets with adverse selection. When there are two selection markets in which consumers select based on the same piece of private information, then allowing firms to write contracts across both markets, i.e. tying con- tracts, can substantially improve welfare by preventing unravelling. We show this by considering two markets with adverse selection where: i)agents have multiple dimen- sions of private information: on their expected cost to the firm as well as on their risk preferences. ii)selection is driven by private information on a characteristic which is also relevant in the other market iii) firms compete not only on price, but also on the terms of the contract. We show that in this setting a perfectly competitive equilibrium always exists and tying contracts are always used in equilibrium. Tying contracts serve one of three roles: 1) screen based on risk preferences, or 2) screen based on expected cost, or 3) act as pooling device essentially allowing consumers to cross-subsidise their insurance. Tying contracts can thus prevent unravelling by e.g. attracting risk averse agents of all cost types while individual contracts would have attracted high cost types of all levels of risk aversion leading to unravelling. Thus, this framework suggests that tying contracts may be a market-based solution to the problem of markets unravelling due to adverse selection and does not require public funds.This framework also provides a rationale for the co-existence of contracts which previous theories could not explain.