We performed a study of the giant magneto-impedance effect and its characteristics in nearly zero magnetostrictive glass-covered amorphous wires and in such wires after glass removal at frequencies between 1 kHz and 10 MHz. The results were compared with those obtained for a cold-drawn amorphous wire with the same composition. We also analyzed the dependence of the effect's sensitivity in these samples on the operating frequency. The observed behavior was explained in terms of magnetic domain structures and circumferential permeability behavior at high frequencies, by considering also the skin effect.