I agree there are many variables involved in whistles and the people playing them. Much has to do with inherent ability and tendencies we employ from the beginning that feel natural to us…some good and some not so good. When most of us first began playing whistle, there were no teachers or experienced players around to make suggestions how to “approach” it. We just grabbed it, stuck it in our mouths and blew and did what felt natural to us at the time. For many, this has created some awfully bad habits, myself included that I had to break after meeting up with some excellent players who actually knew how to play.
I’ve always been one to “hold” the mouthpiece with my mouth…not biting down or tight…but similar to loosely sucking on a straw and hasn’t been a problem because I’ve always played easy-blowers like Burkes, Sindts, Susatos, etc.
Then came a Chieftain hi D that was nearly impossible to play in the upper register, so it stayed in my bag. I couldn’t play that thing to save my neck. Then I got the Overton from Doc. It was a bit easier to play than the Chieftain but I still had problems with the second octave and got that hard, buzzy tone in the first octave. At that point I contacted Colin asking for help on how to approach playing an Overton. Brigitte replied with some suggestions that completely changed things. As both Brigitte and Colin pointed out in this thread, relaxing and simply resting the mouthpiece on my lower lip without holding it tightly in my mouth as I used to do, changed the tone completely and enabled me to easily and relatively effortlessly hit nice pure notes into the third octave. It sounded like a completely different whistle and much easier to play with a nice smooth, pure, strong character and no hard edge or buzziness. And as Colin mentioned, if you want to add an “edge”, you can. I’m amazed at what this whistle is capable of by simply altering my style and approach. I’m no great player but I can actually make this Overton sound sweet enough to play airs. Whooda thunk it 
Using this relaxed technique, the Chieftain is no problem through both octaves. It’s actually pretty easy to play now with nice clarity and a big, fat sound that’ll be good for very loud sessions.
Like Doc, using the “relaxed” mouth technique, I haven’t experienced much if any improvement playing my Burkes or Sindts, I think because they’re so easy to play to begin with no matter how you hold your mouth. You blow, and you get a nice pure tone through both octaves with minimal effort. That’s what Burkes and Sindts do.
Doc didn’t see any improvement using this technique with Overtons, but all I know is I sure did with this Overton. And it made a huge difference with the Chieftain that I really like now. Here again is the variable aspect. We’re all different and what may work for one player may not work for the next.
DC
).