FINEMET-type (Fe75Si15NbBCu) ribbons were heat treated, and their magnetic properties were analyzed. Permeability, thermal, and mechanical sensitivities were measured by commonly used industrial methods, and these properties were correlated with measured magnetic Barkhausen noise parameters. Distributions of peak area, A, and peak noise energy, E, were evaluated. Distribution functions of noise parameters, P(x), were in good agreement with the theory of self-organized criticality (SOC), satisfying power laws in the form P(x)similar to x(-alpha). It is found that the noise did not considerably depend on the temperature sensitivity parameter and on the permeability of ribbons. However, a useful correlation between the noise parameters and mechanical sensitivity has been observed. Minimal noise was detected for samples with negligible mechanical sensitivity in an amorphous-nanocrystalline composite state obtained by a heat treatment at 853 K.