I have a couple of inexpensive whistles. A few days ago I noticed that one of them, a Feadóg was unusually sensitive to overblowing and tended to break into the third (!) octave. For a while I thought it was because my other whistle, a tweaked Clarke Sweetone had higher air requirements, and I needed to learn how to blow differently on each whistle. That's true to some extent, but I was finding it difficult to even play a long high G without getting a "warbling" sound due to the third octive breaking in a little.
Then I remembered reading a description of a similar problem on the Chiff and Fipple forums, which, according to the writer, was resolved by removing debris from the fipple. So I removed the Feadóg's fipple and, sure enough, there was a thin strip of plastic projecting from the bottom. I don't know if it was a manufacturing defect or if I created it by scraping the side of the fipple with the edge of the body while tuning the whistle, but I suspect the latter since the problem just appeared. I removed the burr with a thin kitchen knife and the whistle now sounds quite a bit better.
By the way, the Feadóg and the Sweetone have very different sounds, and both are quite pleasant. I would guess that this is mainly due to the conical vs. cylindrical bodies. They're very inexpensive, so if you've tried only one style of whistle body it might be worthwhile to have at least one of each.