Few complete human genomes from the European Early Upper Palaeolithic (EUP) have been sequenced. Using novel sampling and DNA extraction approaches, we sequenced the genome of a woman from "Pesxtera Muierii,"Romania who lived similar to 34,000 years ago to 13.5x coverage. The genome shows similarities to modern-day Europeans, but she is not a direct ancestor. Although her cranium exhibits both modern human and Neanderthal features, the genome shows similar levels of Neanderthal admixture (similar to 3.1%) to most EUP humans but only half compared to the similar to 40,000-year-old Pesxtera Oase 1. All EUP European hunter-gatherers display high genetic diversity, demonstrating that the severe loss of diversity occurred during and after the Last Glacial Maximum (LGM) rather than just during the out-of-Africa migration. The prevalence of genetic diseases is expected to increase with low diversity; however, pathogenic variant load was relatively constant from EUP to modern times, despite post-LGM hunter-gatherers having the lowest diversity ever observed among Europeans.