A detailed study of known and new SD bands in Tb isotopes has been performed with the use of the EUROBALL IV gamma-ray array. The high-statistics data set has allowed for the extension of known SD bands at low and high spins by new gamma-ray transitions. These transitions, as it turns out, correspond to the rotational frequencies where the principal superdeformed gaps (Z=66,N=86) close giving rise to up- or down-bending mechanisms. This enables to attribute the underlying theoretical configurations with much higher confidence as compared to the previous identifications. Five new SD bands have been discovered, three of them assigned to the ¹⁵²Tb and the two others to the ¹⁵¹Tb nuclei. Nuclear mean-field calculations have been used to interpret the structure of known SD bands as well as of the new ones in terms of nucleonic configurations.