The replacement hypothesis of modern human origins holds that the original population of modern humans expanded throughout the world, replacing existing archaic populations as it went. If this expanding population interbred with the peoples it replaced, then some archaic mitochondria might have been introduced into the early modern gene pool. Such mitochondria would be recognizable today because they should differ from other modern mitochondria at several times the number of sites that we are used to seeing in pairwise comparisons. In this paper we ask what can be inferred from the absence of these "divergent" mitochondria from modern samples. We show that if the effective number of females in our species has been large for the past 40,000 years, then the level of admixture must have been low. For example, if this effective number exceeded 1.6 million, then we can reject the hypothesis that more more than 2/1,000 of the mitochondria in the early modern population derived from admixture with archaic peoples. We argue elsewhere that regional continuity would be detectable in the fossil record only if the rate of admixture exceeded 76%. Here, we show that this level of admixture would require the effective female size of the human population to have been less than 1,777 for the past 40,000 years.