A few star clusters in the Magellanic Clouds exhibit composite structures in the red-clump region of their colour–magnitude diagrams. The most striking case is NGC 419 in the Small Magellanic Cloud (SMC), where the red clump is composed of a main blob as well as a distinct secondary feature. This structure is demonstrated to be real and corresponds to the simultaneous presence of stars which passed through electron degeneracy after central-hydrogen exhaustion and those that did not. This rare occurrence in a single cluster allows us to set stringent constraints on its age and on the efficiency of convective-core overshooting during main-sequence evolution. We present a more detailed analysis of NGC 419, together with a first look at other populous Large Magellanic Cloud clusters which are apparently in the same phase: NGC 1751, NGC 1783, NGC 1806, NGC 1846, NGC 1852 and NGC 1917. We also compare these Magellanic Cloud cases with their Galactic counterparts, NGC 752 and NGC 7789. We emphasise the extraordinary potential of these clusters as absolute calibration marks on the age scale of stellar populations.