The Neolithic transition has led to marked increases in census population sizes across the world, as recorded by a rich archaeological record. However, previous attempts to detect such changes using genetic markers, especially mitochondrial DNA (mtDNA), have mostly been unsuccessful. We use complete mtDNA genomes from over 1700 individuals, from the 1000 Genomes Project Phase 3, to explore changes in populations sizes in five populations for each of four major geographical regions, using a sophisticated coalescent-based Bayesian method (extended Bayesian skyline plots) and mutation rates calibrated with ancient DNA. Despite the power and sophistication of our analysis, we fail to find size changes that correspond to the Neolithic transitions of the study populations. However, we do detect a number of size changes, which tend to be replicated in most populations within each region. These changes are mostly much older than the Neolithic transition and could reflect either population expansion or changes in population structure. Given the amount of migration and population mixing that occurred after these ancient signals were generated, we caution that modern populations will often carry ghost signals of demographic events that occurred far away from their current location.