Until recently I had never even heard of the button type cocking piece. (doesn't mean much as I don't know that much about LEs) Then a few years back, I picked up two LE's, a No,1 and a No.4. The No.1 came with two bolts, each of them with the button. Due to head space issues, I picked up a third one. It too was the button type. Oddly, the No.4 also came with the button type.

I don't have anything interesting to add about them, just verifying that there are a few of them out there for the No.4.