In even-mass Te isotopes with 114 <= A <= 122 the experimentally observed yrast I-pi = 16(+) states have been interpreted as favored noncollective oblate states based on the fully aligned pi[(g(7/2))(2)](6+) circle times v[(h(11/2))(2)](10+) configuration. For Te-124 the highest-spin positive-parity state known has I-pi = 10(+). An extension of the yrast cascade of Te-124 is needed to spin at least 16(+) in order to answer the question of whether this noncollective oblate state lies along the yrast line in this isotope. The level structure of 124Te has been studied via prompt gamma-ray spectroscopy. Te-124 was produced in the fission of the compound systems formed in two heavy-ion-induced reactions, Mg-24 (134.5 MeV) + Yb-173 and Na-23 (129 MeV) + Yb-176. gamma-ray spectroscopy was accomplished with the Gammasphere array. The yrast cascade of Te-124 was extended up to 5481-keV excitation energy with a tentative 16(+) assignment for the highest observed state. This state does not exhibit the characteristics of the favored noncollective oblate states with I-pi = 16(+) observed in the lighter doubly even Te isotopes, indicating that such a state is probably no longer yrast in Te-124.