Two complete data sets of the dependence of dielectric permittivity on temperature and frequency in the range of 10-3 to 109 Hz are reported for K1-xLixTaO3, x=0.025 and x=0.033, with two impurity-induced relaxation branches observed in detail. It is shown that in the x=0.033 samples, relaxation in the low-frequency branch crosses over from random-barrier to hierarchical behaviour as the temperature is lowered. For the first time the authors fit the expressions describing each type of relaxation to both depolarization current and dielectric permittivity data, allowing a crossover temperature to be determined. In addition, a detailed study of the high-frequency branch gives a new insight into its quite particular behavior. It is also shown that within experimental error, the dielectric properties of the sample do not depend on the method of growth.