We have measured the conductance of atom-sized contacts of dilute MgZnCa and MgZnCe alloys at room temperature (RT) and found two new peaks at (1.6–1.7)G0 and (2.6–2.9)G0 (where is the quantum unit of conductance) in their conductance histograms. Because the solute level in these alloys is too low to affect the contact conductance, these peaks can be considered as low-conductance peaks of pure Mg, which have not been observed in the histogram of pure Mg at RT [Smit et al., New J. Phys. 11, 073043 (2009)]. The MgZnCa and MgZnCe alloys differ from pure Mg primarily in their superior ductility. Thus, the observation of new peaks for these alloys suggests that the absence of low-conductance peaks below 4G0 in the room-temperature histogram of pure Mg is likely related to the plasticity of Mg.