In all this time of practicing, I now I have a pleasant, consistent first octave on my Gen High D. For the 2nd octave, D, E and F# sound pleasant (well, as pleasant as 2nd octave can sound), but then the trouble starts. G is mostly, kinda there, and then it all falls apart. 2nd A, B and C# end up sounding very windy, raspy and shrilly, nothing like the cleaner 2nd octave of the lower 3 holes.
I have tried to adjust my breath control, but no luck with that yet.
What should I try next?
A Dixon trad 
Seriously, I find the Gen D very difficult to play above a G. Others clearly don’t have this problem though.
Well, you might have a very valid point. Maybe I just need to take more time and eventually the 2nd G+ will sound better for me. Or maybe my Gen High D will never sound good that high and a new whistle is needed. Considering what I’ve read on this forum about the randomness of Generation whistles…
My suggestion:
Find someone who is a good whistle player see if they can play the notes differently
Boyd
“Plain” (i.e. non-tweaked) Generations are somewhat notorious for the problem you describe. You can: 1 - get yours “tweaked” by someone who knows what they’re doing (Jerry Freeman jumps to mind) or 2 - buy a tweaked whistle (hmmm… Jerry comes to mind again) or 3 - buy a higher-end whistle (Burke, etc) or 4 - buy a Clarke or 5 - just live with it. I went the expensive route (Burke and Parks), but that may not be the best solution for everyone…
Pat
Gens are fabric-made and therefore one is lucky if there’s a good one. So the problem can be that it’s a bad whistle. Just as probable is that you still beat the problem after more practise. The highest 3 notes on the 2nd octave are hard to blow and even harder on a whistle like a Gen. But if you learn to manage, you can blow any whistle.
I am going to be a cheap skate and see if I work through the oddness, since the odds are just as good my inexperience could be the problem.
As you go to the higher notes, you need to move less air faster through the whistle. You do this by pursing your lips and making your mouth cavity smaller. Think of blowing a slender stream of air through the airway faster. Once you get the knack, you’ll find the high notes sound cleaner and less shrill. With practice, you’ll find the volume comes down a bit.
Conversely, the lower notes sound better if you move more air through the whistle slower. Drop you jaw a little and make your mouth cavity larger; think moving a thick stream of air through the whistle slowly. You probably are already doing this right since the low notes sound OK.