Significance Understanding when Neanderthals disappeared is a hotly debated topic. When radiocarbon dating placed the Spy Neanderthals amongst the latest surviving in Northwest Europe, questions were raised regarding the reliability of the dates. Using a procedure more efficient in removing contamination and ancient genomic analysis, we show that previous dates produced on Neanderthal specimens from Spy are too young by up to 10,000 y. Our direct radiocarbon dates on the Neanderthals from Spy and those from Engis and Fonds-de-Forêt show a reduction of the uncertainty for the time window corresponding to Neanderthal disappearance in Northwest Europe. This population disappeared at 44,200 to 40,600 cal B.P. (at 95.4% probability). This is also earlier than previous suggestions based on dates on bulk collagen.