Thallium bromide (TlBr) is an attractive material for high-energy radiation detection applications due to its high molecular weight and relatively large band gap. Previous studies on acceptor doping with Se and S revealed limited solubility of the acceptor dopant in the TlBr crystal, leading to long term changes in dark ionic conductivity, and, presumably, detector sensitivity and performance. Here, the ionic conductivity of TlBr acceptor doped with the larger ionic radius Te2- (2.21 angstrom versus 1.98 angstrom for Se2-) is studied using impedance spectroscopy. Due to the low concentration of Te, in contrast to Se or S doping, acceptor dopant-defect association was not observed. Acceptor exsolution was confirmed at temperatures below 100 degrees C by following changes in ionic conductivity with time. The time constant and activation energy (0.27 +/- 0.14 eV) for exsolution of Te are considerably lower than that of Se, with the mechanistic origin of the activation energy related to Br migration, in marked contrast to that of Se exsolution, which is controlled instead by Tl migration, as discussed here. This long term, time-dependent change in dark resistance could negatively impact radiation detector sensitivity and therefore acceptor doping should be avoided. (C) 2013 Elsevier B.V. All rights reserved.