The Air Buddy Octopus, a big improvement over the old kind.
Look at the Air Buddy in the picture.
It is the tiny black mouthpiece to the right of the normal regulator second stage.
Actually, if you don't count the large chrome mounting nuts which are identical to those on a normal 2nd stage, all you can see of the Air Buddy is the silicone mouthpiece.
All the functioning parts are hidden inside where they cannot get in the way.
Here's what it looks like mounted on your regulator.
You see it mounted in its normal position on the end of the yellow octopus hose of the regulator in the picture. It obviously eliminates all the problems caused by the bulk of an extra normal 2nd stage hanging on your regulator. It does not eliminate the hose. It makes the hose less of a problem.
If you leave your octopus trailing behind, it cannot get caught in coral, mono-filamant line or fishermen's nets.
If you tuck it into your BCD, you can tuck it under any strap or stick it in any pocket and it will pull free in an emergency without ever hanging up.