[en] The giant magnetoimpedance (GMI) effect and its field sensitivity (η) have been studied in Co₆₉Fe_4.5X_1.5Si₁₀B₁₅ (X=Ni, Al, Cr) amorphous ribbons in the frequency (f) range of 0.1-10 MHz. It is found that at f<5 MHz, the GMI effect and η reach the largest values for the Al-containing sample and the smallest values for the Ni-containing sample, while an opposite trend is observed at f>5 MHz. Magnetization and atomic force microscopy (AFM) experiments reveal that the largest values of the low-frequency GMI effect and η for the Al-containing sample result from the largest value of magnetic permeability, while the largest values of the high-frequency GMI effect and η for the Ni-containing sample are attributed to the smallest surface roughness of this sample. These results point to the importance of the sample surface in determining high-frequency GMI behavior. A correlation between the sample surface and high-frequency GMI is established in the investigated ribbons.