Taking the head off doesn’t do anything in and of itself, other than make the whistle slightly tunable, (by allowing the head to slide up and down). The fundamental tweak is to put a small wad of something like sticky-tack (AKA fun-tack or blue-tack) in the hollow space under the windway of the fipple piece. This generally improves the tone some, and rarely hurts. (This doesn’t apply to whistles, like the Clarke, that employ a plug). Use the search, and you’ll find a variety of threads where tweaking is discussed.
Just in case you don’t want to search, a standard tweak involves filling the area below the windway with poster putty, very gentle sanding inside of the windway itself to remove any excess plastic, and taking a few strokes to the labium with a file. Pretty much anyone can do that effectivly.
Then there are also people like Jerry Freeman and Tommy Dion who do professional level tweaks on whistles. These tweaks involve adding pieces and doing all sorts of crazy stuff that make them sound awesome from what I hear.
I was watching this video: http://www.youtube.com/watch?v=2xTZcdoOjjs
where Davy Spillane plays what seems an Overton Low F, when I’ve become aware that it has a piece of tape covering part of the upper 3rd hole.
What’s the purpose of this tweak?