In Australia, as in many other parts of the world, open access is the default policy setting for most protected natural areas, including World Heritage sites. This is despite considerable evidence that unrestrained levels of visitation can be unsustainable in terms of impact on the environment and recreational experience. This paper seeks to answer two questions. First, to what extent are visitors willing to forego access to publicly owned protected natural areas in order to ensure less crowding and/or better environmental outcomes? And second, if access were restricted, how would visitors like remaining access rights to be allocated? The results show that visitors are, in general, willing to trade off some degree of access rights for better environmental outcomes and reduced crowding; particularly the former. It is clear that peak pricing is not supported, whereas visitor caps have broad support.