I was just at a friends house playing and talking music…(note: the fact that I have found people to do this with thrills me to no end). It was one of those wonderful houses that seems to have instruments wherever you look…and then, in a box of percussivey things, there it was. An in the box, barely played Clarke original in C. Just calling out to be loaned out and loved for a week or so, by someone who has never played a Clarke original. It’s fun, and really different from the oak and feadog that are my friends right now, but I’m having a really hard time getting a clean 2nd octave. Is there a trick to it other than smooshing the windway (bad protocol on a borrowed whistle and all)? I find I’m kind of doing the same thing by tightening my lips on the 2nd octave.
That sounds about right. 
Just keep playing it and pay attention to how you sound, not the technique you’re using. Within a few days you still won’t know how to do it, but your lips will know, and you will never have to think about it again.