The influence of drawing tension on the formation of Bragg gratings in B-Ge- and Sn-Ge-codoped core fibers is investigated by transmission and stress measurements. With increasing drawing tension, the axial stress is reduced in the B-Ge-codoped core but increased in the Sn-Ge-codoped core. A higher drawing tension leads to a photosensitivity enhancement and an increase of the core stress during the grating formation in B-Ge-codoped fibers. For Sn-Ge-codoped fibers, increased drawing tension results in an UV-induced stress decrease accompanied by a reduction of the photosensitivity. The results are discussed on the basis of an UV-induced compaction of the core network