The mechanisms that limit the power loss performance in melt-spun amorphous ribbons have been investigated through DC and AC magnetic characterization methods. The measured total power loss is resolved into hysteresis, eddy current, and anomalous losses. The anomalous loss is found to account for more than 90% of the total loss, which significantly reduced by annealing in a transverse magnetic field. This is attributed to the reorientation of preferred magnetisation axis perpendicular to the length of ribbons. Transverse magnetic annealing promotes the relative contribution of domain rotation over domain wall motion during magnetisation reversal process. Magnetic annealing also causes a measurable decrease in the domain width, which promotes pinning and inhibits domain wall motion, thus further favoring coherent domain rotation as the primary mechanism of magnetization. This combination accounts for a 75% decrease in the total power loss in the so-processed ribbons and renders them attractive for applications in mid-and high-frequency power supplies and inverters.