A while ago, I posted some instructions on eliminating the shrill squeal of the high notes (http://chiffboard.mati.ca/viewtopic.php?t=30644&highlight=shrill):
“Getting rid of the buzz and the loud high B: Some whistles have loud unpleasant overtones on the high notes. I suspect this comes from the corners where the blade of the fipple meets the walls. Take two bits of bees’ wax (poster-putty will do), about the size of a grain of rice, and work them into the corners at the ends of the blade. You may need something to help get the wax into the corners, a pencil, or a biro will do. Again, it is trial and error, but you will get there. The effect is that the whistle gets a bit sharper (luckily you can adjust the fipple), a bit quieter, the low notes may become quite soft and too easy to overblow (less wax on the blade should fix this), the high notes get sweeter, and the octaves may be improved.”
I promised I’d post some helpful pics. Here they are:

A C-whistle tweaked with beeswax.

Close-up of the beeswax.

A D-whistle tweaked with cobbler’s wax. Cobbler’s wax is a bit stickier and is easier for doing fine adjustments.
Toot sweeter!
P.