I haven't given greenies to my littlest pup. And when I gave them to my older pup it wasn't very often and it was completely supervised. I watched him one time eating the greenie and it was the teenie tiny size and he basically had whittled it down to a small stick so it was no longer in the tooth brush shaped and then it was gone the next time I looked over. I was perplexed until a minute later he coughed and choked the entire thing back up.
I realized then that they don't always chew them up first, they just inhale them. It was at that point that I stopped giving my pup the greenies. Not sure if I will give them to them again.
