Core rod sections useable for production of finished optical fiber preforms are fabricated by inserting one or more core body pieces axially end-to-end inside a glass cylinder, thereby defining joints between adjacent ones of the inserted pieces. The cylinder is mounted with the contained core body pieces in the region of a furnace. The glass cylinder and core body pieces are heated together in the furnace, thereby elongating the cylinder and the core body pieces contained in the cylinder, and the cylinder collapses to form a finished core rod. Core rod sections are cut from the finished core rod at positions that coincide with the joints between the core body pieces. One or more of the cut core rod sections are useable for the production of optical fiber preforms.