We have a new gripper in our store, called The Pincher Grip...BUT, I dislike associating the word "pinch" when holding a pencil, so I'm choosing to call it The Thumb Grip.
The Thumb Grip (my name) or The Pincher Grip (it's real name)
Grip Starter Set
This gripper is similar to the Crossover Grip, but does not have the "hood". I think it does a good job of discouraging the crossing over of the thumb and is more accommodating for children with long fingernails. It just might replace the Crossover Grip, at least that's what I'm finding. The manufacturer sees it as a transition from the Crossover Grip > Pinch Grip > Pencil Grip. I believe that children can go from Pinch Grip (Thumb Grip) to no gripper.
Our popular Grip Starter Set now comes with a Thumb Grip. (We replaced the Crossover Grip with the Thumb Grip.)
The Crossover Grip