Just want to talk about long *ī and *ū in Proto-Indo-European (PIE) and to assert boldly that they don't exist at all. Yes, methinks that some of you have been fooled by that blasted Pokorny again, so let me explain.
Since Laryngeal Theory finally gained popularity way back in the 1950s, it was finally understood that many of the instances of what were once believed to be *ī and *ū were reanalysed as *iH and *uH (where *H equals one of the three laryngeals proposed in the now-standard theory) and I'm not the only one that dismisses long vowels altogether.
First of all, we need to tell all of our language-loving friends and neighbours of the wonderful news that even the short counterparts *i and *u don't exist much in PIE as anything other than allophones of the consonants *y and *w. Oh yes, of course they exist phonetically. However, as distinct phonemes? Not quite.
So what's the reason for the hold-out against Laryngeal Theory? Why not just confess outright that there are no long high vowels in PIE at all? You really can't win, my stubborn denialists. It seems that some people are basing their antiquarian notions on a few cited reconstructions of long high vowels such as *tū "you", *nū/*nūn "now" and *mūs- "mouse". However, for starters, there's no proof that *muh₁s- is not the underlying stem for "mouse" and surely for the sake of Ockham's Razor, this is more desirable as a theory if it can be shown that *ī and *ū are entirely unnecessary in the two preceding words as well as all other similar forms. It's even more desirable if it turns out that this word is a derivative of an onomatopoeic stem *muh₁- "to mutter". Sihler seems to want to side with Ockham's Razor and say no to the Dark Side, but still needs a boost of encouragement from readers like me. If the old genitive form of this stem, *mūsós, is not enough encouragement showing that a persistently long vowel in a deaccentuated syllable is the big smoking gun of a laryngeal at work, then I don't know what is.
With *tū and *nū(n), it's important to notice that they are both particles. Variation in the pronunciation of particles based on context is a universal theme in languages. For example, in English, the indefinite particle "a" is normally pronounced as a schwa in many dialects, unless one wants to emphasize the indefiniteness of the object (e.g. "a man", as in "one of many men", opposing "the man"), in which case we hear an audible shift in stress by the speaker onto the particle itself and also a change in pronunciation of its vowel to something like Canadian English /ɛj/. Thus an innocent particle like "a" has two variants of pronunciation, one for emphatic, the other for non-emphatic. Same thing goes for "the" which is normally pronounced /ðə/ unless emphasized to /ði/ (e.g. "The Tony Blair is coming to dinner?? Where did I put my fine china?!"). In French, the nominative 2ps pronoun tu is pronounced /ty/ (although often reduced to /t(ə)-/ in everyday speech) but the accusative form "te" is nothing but a reduced form of the latter, pronounced as /tə/. This is common throughout the world and I have no doubt it could have occurred in pre-PIE, PIE itself and post-IE, shifting with the changing phonology.
The fact is that *tū and *nū(n) can just as easily be reconstructed with short vowels, thus *tu and *nu without even a need to posit a lost laryngeal in these cases, because if particles can often vary between emphatic and non-emphatic forms, there is enough doubt then in the existence of these forms with long high vowel in PIE proper, and it all starts to seem like a careless diachronic mixup. Instead, I find it likely that long vowels in these words developed in variant forms after the sound change of PIE *iH and *uH to *ī and *ū respectively in descendent dialects. With the vowel inventory expanded by this change, logically, such languages would be free to create alternative forms of some of these particle words with new long vowels that previously never existed.
And so, modern Indo-Europeanists can wave a tear-filled adieu to our friends, **ī and **ū. It's been a blast. Now, bon voyage.
 Lehmann, Theoretical Bases of Indo-European Linguistics (1993), p.109 (see link); Meier-Brügger, Indo-European Linguistics (2003), p.76 (see link).
 Lehmann, Theoretical Bases of Indo-European Linguistics (1993), p.106 (see link).
 Lehmann, Theoretical Bases of Indo-European Linguistics (1993), p.107 (see link).
 Lehmann, Theoretical Bases of Indo-European Linguistics (1993), p.111 (see link); Meier-Brügger, Indo-European Linguistics (2003), p.83 (see link); Fortson, Indo-European Language and Culture: An Introduction (2004), p.61 (see link).