Minor elements, when added to binary amorphous alloys in small percentages, can often lead to significant improvements in both the plasticity and glass-forming ability (GFA) of the alloys. Considering that plasticity and GFA are two contrasting properties dependent on short-range orders (SROs) of differing degrees, this experimental observation at first seems paradoxical when considered from an SRO viewpoint. In this study, comparative studies on amorphous alloys Cu50Zr50 and Cu47.5Zr47.5Al5 were performed using experiments and simulations to elucidate how these two apparently mutually exclusive properties can be realized at the same time. Using molecular dynamics simulations, we resolved the local structures of Cu50Zr50 and Cu47.5Zr47.5Al5 in terms of icosahedral medium-range orders. In addition, the role of the minor element (Al) on the formation of the icosahedra and their medium-range structures during cooling, as well as their disordering behavior during subsequent plastic relaxation, was clarified.