Found at Dienekes and Mundo Neandertal.
The Pääbo team, that already delivered on the first sequenced Neanderthal genome of Vindija cave (see this and this previous posts), has managed to mass-copy and analyze five more Nenderthal mtDNA sequences.
Their conclussions are that Neanderthals had much lower mtDNA diversity than modern humans and even lower than modern Europeans. Two of the sequences are in fact identical (Feldholder, Neanderthal-1 of Germany, and Vindija, Croatia) meaning they were close relatives by maternal side.
They estimate an effective population size of 1500 to 3500 women in Europe (no Asian Neanderthals have been studied so far). They also believe that the "Neanderthal Eve" would have lived some 120,000 years ago.
This is more recent than the "Homo Sapiens Eve" but would still be much older than the European or even Eurasian "Eve" (L3) by the usual estimates.
The sequences studied are from El Sidrón (Asturias, Spain), Feldhofer (Nordrhineland-Westfalen, Germany - Neanderthal 1), Vindija (Croatia - 2 sequences with the other specimen studied before) and Mezmaiskaya (Caucasus mts., Russia - 2 sequences as well).
Original paper: Adrian W. Briggs et al., Targeted Retrieval and Analysis of Five Neanderthal mtDNA Genomes. Science 2009. Behind paywall, supplemental material freely accessible.
Divlugative article at Live Science.