The ground system of levels of Tb I belonging to the electron configuration 4ƒ85d6s2 has been extended with 8H92, 8H152, 8H172, 8G12, 8F12 and 8F32 by systematic searches making use of new Zeeman effect measurements. The first two of these levels provide a reliable check on the odd 152-levels published previously and they also allow to establish two more 152-levels as well as two odd J = 172 levels. The 8G12 level is interesting because of its large negative g-factor, giving rise to peculiar Zeeman patterns which served to locate a number of new odd levels with J = 12 and 32. Likewise the discovery of 8F32 is closely connected with the establishment of new odd levels having J = 12. In total 34 new odd levels have been established and the list of classified lines is extended by 434 lines, making a total of 2647, after cancelling a few previous classifications. Some details of the procedure used in establishing the levels with extreme J-values are discussed and a description is given of the evaluation of the Zeeman-spectrograms in order to derive the maximum amount of useful information out of the perturbed patterns.