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I’m not sure how you can train yourself to not reach so high, but I know that your fingers only need to come up enough so that the hole isn’t covered… some players play with high action, others with low action… Whatever’s comfortable, I’d say, although I’d try to avoid lifting them up too high…
Some of it is speed capability, along with accuracy in getting the finger back down on the hole. Some is pure comfort. Personally, I try to raise my fingers just far enough to get the proper sound from the whistle (hang too close and the pitch alters). As I tire, I find my fingers getting higher off the holes.
Here’s a simple stretch for your carpal tendons:
- Drop your right arm, elbow at your side, and bend your right elbow so your right hand raises to 90 degrees with your body.
- Drop the fingers of your right hand down as far as you can.
- Using your left hand, press evenly against the fingers of the right, toward your back. until you feel the carpal tendons stretch almost to the point of discomfort. Hold for 20 seconds.
- Repeat on the left arm.
If you’re keyboarding an mouseing, you should do this stretch about 3 to 4 times per day.
Cheers,
serp
One way to train your fingers if you don’t like how high they are going is to play with your hands under a board of some sort so if they go to high they will hit the board. Or…you could try rubberbands…find a way to rubberband your fingers so they will go only as high as you set the rubberbands for. LOL…but if you poke an eye out don’t blame me.. 
my teacher always held a ruler with tacks in it above my fingers to teach me not to lift 'em too high, but that’s probably a bit too masochistic for the average whistler…
You want to lift them as LITTLE as possible. Try it slowly until you can speed along without flipping all your fingers up. If your fingers move higher than they have to (i.e. whistle doesn’t go flat 'cause your fingers are too low) then you’re putting strain on your tendons, both in your hand and arm.
Your fingers should be relaxed and ALWAYS a bit curved. There are people who play with flat fingers, but it slows you down, and is likely to give you tendonitis if you start playing fast stuffs (as happened to me) 
. Basically, pros can play however they like, and many concert musicians have horrible posture, but bad technique never HELPED anybody. It only makes playing harder. Your call really.
If you play your scales and get progressively faster you will find that your fingers find the right height. As you get faster they will travel less. It is not something I would concentrate on since it will come with experience and practice.
I love your saying about the Celts, very true! As for the fingers, I find that it works either way for me, you could always just glue your fingers to the whistle and play an all “d” song…but…that might ruin the whistle and get you some weird looks.
Why thank you! That is one of my favorite quotes of all time. It came on a little card that was on the back of a Celtic bookmark I bought at the books store.
Are you new, Elven Whistler/Dancer?
Agreed… I know I was much like you, and my fingers were coming off the holes too high… it was driving me nuts that I couldn’t get down my ornamentations, and that was why because it takes too much time if your fingers are travelling too far, and also you are just new to it, and as comfort settles in with your whistle, your arms will relax, your fingers will relax, and suddenly you will find yourself at a comfortable plateau that fits you nicely. Just practice slowly and don’t rush it or over concentrate. It’s easy to get frustrated and tighten up, but try to relax. It’ll happen.
Take care,
John
It doesn’t matter at all, not one little bit, how high your fingers come up. If they hit the holes at the right time, that’s all that matters. Just stay relaxed and concentrate on your rhythm, and the finger-height question will resolve itself.
As with saxophones, so with whistles. There are advantages to keeping movement to a minimum but if you break all the rules, play very well and feel comfortable it would be foolish to try to change.
I’m not sure that it is wise to aim at lifting fingers consistently to a certain height. There are many different ways to half hole and, with notes like F natural on a D whistle, you’ll eventually want to use quite a few, your choice in each case depending on where you’ve come from and where you are going to. I think that different ways of half holing require different lifting heights to feel comfortable.