This paper develops a model of child custody based on an incomplete-contract approach tothe allocation of property rights. Because of the presence of transaction costs in marriage,altruistic parents cannot contract upon the investments they make into their children, but canreduce the resulting inefficiencies by determining ex ante the parent who would be allocatedcustody in case they divorce. We show that: (i) the optimal allocation of custodial rightsdepends on both preferences and technological factors; (ii) custodial rights can be allocatedeither to the parent who values the benefits from child welfare more or, viceversa, to theparent with the lowest valuation; (iii) if one parent’s investment is significantly more importantthan the other parent’s investment, then sole custody is preferred to joint custody and itshould be allocated to the parent whose investment is relatively more important; and (iv) ifthe importance of the parents’ investments is sufficiently similar and if the differences inparents’ valuations of child quality are large, then joint custody is optimal with the lowvaluationparent receiving a relatively greater share, because the other parent would invest inthe child anyway while the low-valuation parent would be endowed with greater bargainingpower. The implications of these results are then interpreted in the context of current custodylaws, discussed in relation to empirical estimates of some of the parameters underlying theoptimal custody rule, and used to question the skepticism surrounding prenuptial contracts.