This paper discusses the scope for market mechanisms, already established for greenhouse gas mitigation in Annex 1 countries that ratified the Kyoto Protocol, for implementing "net mitigation," defined here as mitigation beyond Annex 1 countries' formal mitigation requirements under the Kyoto Protocol. Such market mechanisms could be useful for establishing and extending greenhouse gas mitigation targets also under the Paris Agreement from December 2015. Net mitigation is considered in two possible forms: as a "net atmospheric benefit," or as an “own contribution” by offset host countries. A main conclusion is that a “net atmospheric benefit” is possible at least in the short run, best implemented via stricter baselines against which offsets are credited; but it can also take the form of offset discounting whereby offset buyers are credited fewer credits. The latter, although generally inefficient, can be a second-best response to certain imperfections in the offset market, which are discussed in the paper. There is less merit for claiming that "own contributions" can lead to additional mitigation under existing mechanisms.