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Dielectric properties are reported for lead magnesium niobate (PbMg_1/3Nb_2/3/O₃) ceramics which were prepared as single phase (i.e., without pyrochlore) with an improved technique. Dielectric constants of 18000 for pure PMN and 31000 for PMN with 10% PbTiO₃ were achieved; these values are 50% larger than those reported in the literature. The dielectric constant of PMN ceramics was found to increase with both sintering temperature and excess MgO, and subsequent analysis of the microstructures confirmed that this was due to an increase in grain size. This grain‐size dependence is explained as a consequence of low‐permittivity grain boundaries.