In this paper we analyse the efficiency impacts of different property right allocations when one action produces a private and a public good. There are three players: an environmental agency, point-source emitters and diffuse emitters. We assume a diffuse emitter can undertake one action that produces two outputs: one he can sell to the environmental agency (a public good); and the other he can sell to point-source emitters (a private good). We analyse the efficiency implications of allocating the property right of the private good to either: (i) the agency, since in buying the public good the private good is produced as a by-product; or (ii) the diffuse emitter. Generally, the latter improves the efficiency outcome.