On the other hand...Neanderthals gave us disease genes
Gene types that influence disease in people today were picked up through interbreeding with Neanderthals, a major study in Nature
They passed on variants involved in type 2 diabetes, Crohn's disease and - curiously - smoking addiction.
Asked whether our ancient relatives actually suffered from these diseases too [except, of course, smoking addiction], or whether the mutations in question only affected the risk of illness when transplanted to a modern human genetic background, Mr Sankararaman said: "We don't have the fine knowledge of the genetics of Neanderthals to answer this," but added that further study of their genomes might shed light on this question.
However, some regions of our genomes were discovered to be devoid of Neanderthal DNA, suggesting that certain genes had such harmful effects in the offspring of modern human-Neanderthal pairings that they have indeed been flushed out actively and rapidly through natural selection.
"We find that there are large regions of the genome where most modern humans carry little or no Neanderthal ancestry," Mr Sankararaman told BBC News.
"This reduction in Neanderthal ancestry was probably due to selection against genes that were bad - deleterious - for us."
The Neanderthal-deficient regions encompass genes that are specifically expressed in the testes, and on the X (female sex) chromosome.
This suggests that some Neanderthal-modern human hybrids had reduced fertility and in some cases were sterile.
Another genome region that lacked Neanderthal genes includes a gene called FOXP2, which is thought to play an important role in human speech.