I was at a session a few weeks ago and noticed another whistle player playing the first part of Morrison's Jig by just lifting fingers two and three of his top hand, while keeping the first two fingers of his bottom hand down nearly all the time (except for the A-F#-E or G). I tried it, and it made the tune really easy to play.
I've been experimenting with Brother Steve's suggestions on "not lifting a finger" lately with good results. In addition to Morrison's, I'm finding his advice really useful in The Atholl Highlanders, the Kesh, The Sally Gardens reel, and others. It also reduces the need for stabilizing the whistle with the bottom hand pinkie in some, but not all cases — I still find the pinkie useful in cases like the second part of "Drowsy Maggie" where you alternate between C# and high E.
This is one of many cases where I read something (in this case, Steve's page on this topic) long ago, tried it, and found it not terribly helpful, and then tried it again much later with completely different results. When I first tried leaving bottom hand fingers down for notes like B and A I wasn't playing very quickly, so leaving the fingers down didn't really gain me much, and I didn't like the change in timbre. But I'm playing the tunes much more quickly now, so the timbre change is much less noticable whereas the fingering is correspondingly harder!
It's probably generally true that some advice from experienced players requires a certain level of ability to be helpful — not necessarily a lot, but stuff which seemed backwards to me as a rank beginner is making a bit more sense to me now.