Defining "environmental treaty"

The ENTRI environmental treaty database that I mentioned the other day casts a wide net. It has a bunch of things in it that probably pertain to environmental issues, but for with that either wasn't the primary concern (like tariff and trade agreements) or are "environmental" only within what I consider a fairly generous definition (like the convention creating the World Health Organization).

I'm trying to filter out treaties that I don't think are primarily environmental treaties, but that required coming up with my own definition of an environmental treaty. Here's my first-draft stab at that:

Environmental treaties are treaties with the primary purpose of providing for management or conservation intended to prevent, reverse, or compensate for the destruction or degradation of natural public goods.