Mitochondrial DNA is passed intact from mother to offspring.
It is not involved in sexual mixing, so it changes only by the random process of mutation.
The lack of mutations that might have distinguished the DNA of the individuals in question from each other suggests not only a common ancestor, but a relatively recent one.
Further analysis showed also that two of the mitochondrial DNA samples from Chagyrskaya were closer to the Okladnikov boy than to any of the other Chagyrskayans.
And when the team looked at data on y-chromosomes, which pass intact from father to son, as well as their mitochondrial data, they were able to draw some tentative conclusions about Neanderthal communities.
If members of a population mate more or less at random with those of the opposite sex, the so-called coalescence time - how far in the past their most recent common ancestor lived - should be the same for mitochondrial (matrilineal) and y-chromosome (patrilineal) DNA.
The researchers found, however, that the average coalescence time for the y-chromosome was 500 years, while that for the mitochondrial genome was around 5,000 years.
To explain this order-of-magnitude difference, they modelled various possibilities.
The one which best fitted the data was that the Neanderthals of the Altai lived in groups of around 20 individuals, with at least 60% of the females in a group having migrated there from elsewhere.
The size of such groups is similar to that deduced for Palaeolithic bands of Homo sapiens, which probably had around 25 members.
When dealing with humanity's ancestors and cousins it is easy and tempting to over-interpret the scarce data available - and practitioners of the subject have indeed been guilty of doing this in the past.
So these conclusions should be treated with care.
But if nothing else, this study shows that the methods which brought Dr. Paabo his prize have increased the pool of data available for such speculations in an extraordinary way.