@edgarblythe,
Sorry to be a wet blanket on the pun-fest but I believe everyone has some Neanderthal genes in their makeup. Last Christmas my wife gave me a gift from Nat Geo that involved sending a DNA swab to a lab for analysis.
The results tell you, generally, in what regions your ancestors lived, but it also tell you the level of Neanderthal you have in your make up and how it compares to the general population.
My results were that I have less Neanderthal than the general population, but based on what I've read about this discontinued branch of humanity, I don't necessarily think this is a favorable thing.