Multilevel selection is an important organizing principle that crucially underlies evolutionary processes from the emergence of cells to eusociality and the economics of nations. Previous studies on multilevel selection assumed that the effective higher-level selection emerges from lower-level reproduction. This leads to selection among groups, although only individuals reproduce. We introduce selective group extinction, where groups die with a probability inversely proportional to their group fitness. When accounting for this the critical benefit-to-cost ratio is substantially lowered. Because in game theory and evolutionary dynamics the degree of cooperation crucially depends on this ratio above which cooperation emerges, previous studies may have substantially underestimated the establishment and maintenance of cooperation.