Agree here. I have an estimated 10% of Caucasus DNA (as well as 4% trace from the Middle East and 3% trace Jewish - which may be more accurately categorized as West Asian IMO), and all of my immediate ancestry is European (Sicily/Italy, British Isles, and France). Most likely this West Asian ancestral component is within my 50% Sicilian ancestry.

However, what I'm curious about is the likely source of this ancestry in various European populations. It could be a combination of historical migrations and events, but my vote goes to the ancient Neolithic migrations of roughly 6,000-8,000 years ago as the main source, which, when amalgamated with earlier Paleolithic populations (modern close approximations to this most ancient of European strains would be the Basques of the French/Spanish border region or certain Irish/Scottish types), produced modern Europeans. Paleolithic/Cro-Magnon + Neolithic/Caucasus = Europeans of today.

It certainly appears that most Europeans have a lot more of the Paleolithic component in them, but the Neolithic component is there and is especially important in groups like the southern Italians, Greeks, Albanians, and other Balkan peoples. It's no accident that these last groups tend to differ slightly from most other Europeans in phenotypes (of course they're "white" and what not, but they have tendencies that do go in a somewhat West Asian direction at times like a stronger nose, larger eyes, thicker eyebrows, darker hair/eyes, etc. I'm certainly not saying that any of these latter groups look distinctly Middle Eastern in the true sense (they don't), but just that you can see certain tendencies that are more marked because of the on average heavier Neolithic genetic inheritance. Another thing to keep in mind is that the modern populations of West Asia are certainly not the same as those that were the source of the Neolithic expansion into Europe. Plenty of changes and additions to the gene pool have taken place there since then, such as Bedouin Arab migrations from farther south, Central Asian Turkic migrations, the trans-Saharan slave trade, and more. Ancient Neolithic migrants would've looked like basic Mediterranean types that one sees all around the Mediterranean, particularly the eastern Mediterranean. Sorry to ramble on, but it's fascinating.

Interesting snippet in this link: http://www.sciencemag.org/content/310/5750/1016.abstract