I'm currently typing up a grammatical primer of Proto-Indo-European, largely for myself for now. I know that sounds a little neurotic but my philosophy here is that there's no better way of recognizing the flaws in one's reasoning than trying to put every detail of one's thoughts on paper (or in this case, on computer screen). Sufficed to say, it's no wonder that my obsessive-compulsive exercise bore fruit as I predictably got stumped on a few details which challenged me to get to the bottom of things. It's also sufficed to say that many of these issues in question are still being debated by the most clever of Indo-Europeanists.
One of the things I came face to face with the other day was the matter of "the look" of athematic versus thematic verb stems in the earliest stage of Common Proto-Indo-European. Only today have I reminded myself that I might have already solved this puzzle, but first let me explain the conundrum. Jay Jasanoff maintains that thematic present-future stems ending in the characteristic *-e-/*-o- morpheme are originally subjunctives marked by the same morpheme. I've come to agree with this reasoning since the solution is most trivial and there is indeed a semantic link between subjunctives describing hypothetical situations ('I would go') and verb forms describing future actions which are by their very nature hypothetical ('I am going/I will go').
Yet, for all the careful reasoning and evidence behind this clever solution, Jasanoff's scheme seems to give us a curious overabundance of durative 'Narten stems' (ie. verbs showing *ē/*e ablaut rather than *e/*∅). What's going on? Are the verbs which eventually become 'athematic stems' in non-Anatolian dialects also originally Narten stems? Why don't non-Narten stems outnumber Narten ones which have marked vocalic length? Did Jasanoff make a mistake along the way? Did I? What would have made *h₁ei- 'to go' (3ps *h₁éi-ti / 3pp *h₁y-énti) different from *bʰer- 'to carry' (3ps *bʰḗr-ti / 3pp *bʰér-n̥ti)?
I'd say that while the presence of Narten stems make no sense in PIE itself, it does start to make sense if we understand them as one of the many relics of Syncope in early Late IE when unstressed vowels were deleted. I suggest that while a monosyllabic root when stressed in Mid IE (MIE) of the form *CVC- retained the same structure after Syncope since there were naturally no unstressed vowels in it to vanish, the unstressed final syllable of MIE roots of the form *CVCV(C)- on the other hand was syncopated to produce *CV:C(C)- complete with long vowel due to compensatory lengthening. This must in turn be contrasted with the result of roots of the form *CVCCV- which shortened to *CVCC- with no concommitant lengthening because the onset consonant of the unstressed syllable in this latter example blocked the ability for the disappearing vowel to leap to the previous syllable by simple metathesis as was readily possible in *CVCV(C)- (ie. *CVCVC- > *CVCəC- > *CVəCC- > *CV:CC-).
What my Pre-IE hypothesis has been implying for a while now is that the non-Narten roots in PIE of the simple form *CVC- (eg. *h₁es-, *h₁ei-, *gʰʷen-, etc.) are best derived from monosyllabic roots before Syncope. Narten stems such as *bʰer- however arose only after the syncopation of former polysyllabic verb roots. From this, we may reconstruct monosyllabic roots in late MIE such as *es-, *ei- and *gwen- (for later PIE *h₁es- 'be', *h₁ei- 'go' and *gʰʷen- 'kill') with 1ps/1pp duratives respectively as *és-mai/*as-ménai, *éi-mai/*ai-ménai and *gʷén-mai/*gʷan-ménai. This contrasts with MIE polysyllabic roots conjugated in the 1p like *béra-mai/*bara-ménai which would later become 'Nartenized' to early Late IE *bḗr-mi/*ber-méni before secondarily acquiring acrostatic accentuation in the heart of the Late IE period.
It also tingles me to no end that it just so happens that my predicted monosyllabic root *es- in Mid IE could be further corroborated by the Proto-Semitic existential copula *yiθ 'there is', also coincidentally monosyllabic and thus quite plausibly borrowed into Mid Indo-European during the Neolithic.
 Lipinski, Semitic Languages: Outline of a Comparative Grammar (2001), p.488 (see link): *yṯw 'to be (present)' and its reduced copula form, *yṯ; read also Paleoglot: To be or not to have. That is the question (9 Feb 2008) and Paleoglot: Proto-Semitic as a second language (14 Mar 2008)