A core for winding sheet material is proved. The core comprises a cylindrical tube having a longitudinally oriented slot formed therein, and a strip of soft material located in the slot. Because of the geometry of the slot and the strip, the strip may be softer in the central region but firmer where the core transitions from the relatively soft strip to the relatively hard tube. The leading edge of the sheet material imbeds itself into the soft central region of the strip as additional layers are wound around the core.