The fast ion conductor CuBrTe exhibits structural phase transitions at 230 K and at 351 K. Electrical conductivities of CuBrxCl1-xTe and CuBrxI1-xTe solid solutions were measured in an attempt to discern the effect of chemical substitution on the mobility of Cu+ cations in this compound. In general, the structural phase transitions are found to be accompanied by subtle, second-order electrical phase transitions. In the case of CuBrxCl1-xTe, replacement of Br- with the smaller Cl- anion leads to an increase in room temperature conductivity and a corresponding decrease in activation energy beyond that expected of a proportionate mixing of CuBrTe and CuClTe. By contrast, replacement of Br- with the larger I- anion in CuBrxI1-xTe leads to a decrease in room temperature conductivity and an increase in activation energy proportionate to that expected of a simple mixing of CuBrTe and CuITe.