An ice maker for fitting into a door of a cooling or freezing device includes an ice-making tray which is arranged to be rotatable about an axis of rotation, has a plurality of ice-piece-making cavities and a side wall arrangement which extends upwards beyond the ice-piece-making cavities and runs along the periphery of the tray. The ice maker further includes a drive unit for driving the ice-making tray in rotation about the axis of rotation. At least one slot is formed in the side wall arrangement and passes through the side wall arrangement over its entire wall thickness. Alternatively or in addition, at least a portion of the side wall arrangement is made of a different material than a bottom tray part on which the ice-piece-making cavities are formed. Both measures improve the twistability of the ice-making tray for breaking frozen ice pieces away from the tray.