Božović et al.5 have measured key properties of 'overdoped' high-temperature copper oxide superconductors. a, From their measurements, the authors estimate the superfluid density (red, corresponding to the number of electrons taking part in superconductivity per unit cell; the unit cell is the smallest periodically repeating structure in a crystal) as a function of the doping fraction (a measure of the density of charge carriers). They observe far fewer superconducting electrons than expected from the Bardeen–Cooper–Schrieffer (BCS) theory (green). b, The data are presented here as a plot of the superfluid density against the critical temperature (the temperature below which the material can superconduct). The superfluid density is directly proportional to the critical temperature, over a wide doping range. The authors' remarkable results are incompatible with standard BCS theory and require new explanations.