The problem with greenies is not only that the dog gets a greenie too big for it. The problem is swallowing chunks of the greenie. Sometimes the dog is okay, sometimes it isn't. Some dogs have gotten pieces of greenie stuck in their throat, others have had an obstruction from swallowed greenies.
My IGs love greenies, go crazy for them, I used to let them gnaw on them while I held them, or closely supervised, but even that way Molly managed to break off a chunk of one and swallow it, so I stopped giving them.
On the IG list they were discussing safer alternatives to greenies, and one of the things mentioned were Flossies, made by Merrick. I was already giving them to Mic and to Monte, and they didn't have any problems with them, whether that means they're completely safe or not I don't know.
I also give the pressed rawhide bones to Monte, they're supposed to be the safest kind of rawhide, I use a medium size one he can finish in one session, so I don't have the problem of picking up soggy ones, or him resource guarding it from the IGs, etc.