Usually a ban is the best alternative and indicates purchase by permit; however, the permit would only include those for scientific research, laboratories, and educational venues such as public zoos/aquariums. Considering P. volitans is so wide spread I would see no point in banning the specie either other than banning lionfish as a whole in order to regulate other species from being invasive or in attempt to eradicate the current invasive colonies. Granted there are black market animals, of which Florida seems to be the hub, but U.S. Fish and Wilflife does apply pretty thorough quality control in regards to marine fish and invertebrates to the point of being able to identify coral Genus' and confiscations before animals reach the wholesaler.