Recent work has discussed and formalized the conditions under which liability rules are superior to property rules in a world with "one-sided" incomplete information. These studies demonstrated how liability rules achieve higher social welfare by harnessing one party's private information about its own valuation to the process of optimally allocating the entitlement between the parties. This article introduces a new family of liability rules hitherto neglected by courts and legal scholars. A regime of modular liability rules is one in which the court applies legal rules for which the traditional liability rules are building blocks; these rules harness both parties' private information. Whereas in an efficient liability rule 2 (for example) a polluter is granted a call-option to purchase the right to the air (so to speak) with an exercise price that equals the resident's harm, in modular liability rule 6 + 5 (for example) a pair of options, rather than a single one, is allocated; the resident gets a put option to force a transfer of the entitlement (as under rule 6), but the polluter has a consecutive put option to sell the entitlement back to the resident, if he wishes (as under rule 5). Interestingly, the maximizing joint welfare exercise-price equals, in general and for uniform distributions, an amount that is the average of one party's maximum estimated valuation and the other party's minimum estimated valuation. Two paradigmatic worlds of two-sided incomplete information are studied: a symmetric world, in which the court's best estimate of the parties' private valuations is that they are identically distributed, and an asymmetric world. In the symmetric world, modular liability rules are in some respects more efficient and more fair (exact definitions are discussed in the article) than the conventional liability rules. In the two-sided and asymmetric world, modular liability rules yield higher joint payoffs than regular liability rules if, and only if, the difference between the parties' means is larger than the difference between their amount of private information (represented by the distribution's support). A practical way to implement these insights in real life situations is offered.