The total Qβ-decay energies of 14 nuclides in the vicinity of 132Sn have been measured using high resolution spectroscopic methods. The present results derived for the atomic masses in this region are significantly more precise than the previously accepted values, and differ significantly from these in some cases. The precision of the new mass values surpasses that expected from the systems currently proposed for direct mass measurements of nuclei far from stability. The present results resolve a recently observed and highly puzzling discrepancy between the experimental mass values in the 132Sn region and theoretical systematics.