This article extends the Coase Conjecture to ethical issues of initial acquisitions of property rights. The Coase Conjecture complements the Lockean labour-mixing criterion to limit the boundaries of morally legitimate initial acquisitions of unowned property; whenever the Coase Conjecture applies, the Lockean Proviso that there be "enough and as good" left is automatically satisfied. This holds provided that, when a claim is made, the marginal willingness to pay for the last portion of it is zero (infra-marginally, willingness to pay may be arbitrarily high). Thus, the market price of the claim is zero, except for the part of it that the claimant inhabits or improves. "Excessive" claims therefore come to have a zero market price, so anyone may take possession of them, by purchase or theft. In either case they must compensate the original claimant by a zero amount. It follows that non-claimants do not lose by putatively "excessive" grabs by claimants. This article argues that any initial claims are just under these circumstances.