Domain-wall magnetoresistance and low-frequency noise have been studied in epitaxial antiferromagnetically-coupled [Fe/Cr(001)]_10 multilayers and ferromagnetic Co line structures as a function of DC current intensity. In [Fe/Cr(001)]_10 multilayers a transition from excess to suppressed domain-wall induced 1/f noise above current densities of j_c ~ 2*10^5 A/cm^2 has been observed. In ferromagnetic Co line structures the domain wall related noise remains qualitatively unchanged up to current densities exceeding 10^6A/cm^2. Theoretical estimates of the critical current density for a synthetic Fe/Cr antiferromagnet suggest that this effect may be attributed to current-induced domain-wall motion that occurs via spin transfer torques.