Sometimes you run into a language that has undergone a sound shift that is completely transparent, but at the same time phonetically completely absurd.
One such a sound shift is the shift of Proto-Berber *əβ > Northern Berber *i. Tashelhiyt and Middle Atlas Berber underwent *əβ > *u.
More peripheral berber languages have retained the phoneme *β like Augila and Ghadamès. The Touareg languages generally retain it as h.
Both these shifts are clear, as an example I'll use the word for 'milk'.
PB *aγəβ Augila aγəβ, aγf; Ahaggar ăx; Kabyle iγi; Riffian aγi; Middle-Atlas aγu; Tashelhiyt aγu; Ouargla aγi
This word is somewhat strange in Ahaggar (a Touareg language) as it did not retain the *β as h or even the second syllable at all. One can imagine that *ăxh yielded *ăxx to eventually get shortened to ăx though , but it's not exactly regular.
But as you can see, the small selection of Northern-Berber language clearly shows a perfect proof for the shift *əβ > *i. And citing more examples would simply give more convincing proof for this shit. But now the question is, how on earth does this work?
*β has a labial element so the Middle-Atlas and Tashelhiyt reflexes can be understood as coloring of the schwa to *ŭ and then getting lengthened to *u by compensatory lengething when *β was lost.
Such an explanation of colored vowels can not be used for Northern-Berber though. PB *u is simply reflected as *u in all of them so *əβ did not go through an *u stage before undergoing unrounding to *i. So what if the Proto-Berber sound we *h as found in Touareg rather than *β. We'd get *əh loss of *h could yield compensatory lengthening to *ə̄. As *ə is the high vowel in the short-vowel system, it could be assigned to either of the two high-vowels in the long vowel system.
While the above explanation makes the reflex of Northern-Berber understandable, we've only shifted the problem. Now we are stuck with a shift in Aujila and Ghadamès of *h > β. There's very possiblities to explain such a shift without any conditioning because of rounded/labial vowels in the vincinity.
So there we have it, not a sound correspondence that makes us rethink our theory, but definitely a sound correspondence which is extremely hard to explain phonetically.