We test the hypothesis that the apparent axial ratio of an elliptical galaxy is correlated with the age of its stellar population. We find that old ellipticals (with estimated ages t>7.5 Gyr) are rounder on average than younger ellipticals. The statistical significance of this shape difference is greatest at small radii; a Kolmogorov–Smirnov test comparing the axial ratios of the two populations at R=Re/16 yields a statistical significance greater than 99.96 per cent. The relation between age and apparent shape is linked to the core/power-law surface brightness profile dichotomy. Core ellipticals have older stellar populations, on average, than power-law ellipticals and are rounder in their inner regions. Our findings are consistent with a scenario in which power-law ellipticals are formed in gas-rich mergers, while core ellipticals form in dissipationless mergers, with cores formed and maintained by the influence of a binary black hole.