Method and apparatus for positioning bead cores during a building of a radial tire carcass in a tire-building machine. The method includes positioning first and second bead cores on respective first and second core-centering devices, on a first side of a carcass drum and centering the first and second bead cores. Further, the method includes grasping, with a second core-setting device, the second bead core and transporting the second core-setting device and the second bead core to a second side of the carcass drum. Additionally, the method includes grasping, with a first core-setting device, the first bead core; and setting the first and second bead cores onto the tire carcass by the first and second core-setting devices.