A systematic study of the functional properties of the (1-x)(Bi0.5Na0.5)TiO3–xBaTiO3 (BNT-xBT) piezoceramic system for 0.05 = x = 0.07 is performed. The samples are obtained through the conventional solid-state route. The expected microstructure for these compounds, with no significant dependence on the composition, is verified by field-emission scanning electron microscopy. The morphotropic phase boundary (MPB) is detected for x = 0.06–0.07 by means of the Rietveld analysis of X-ray diffraction data. The dielectric spectra show a frequency-independent, completely diffuse phase transition with a composition-dependent diffusivity coefficient. The depolarization temperature is effectively evaluated from pyroelectric measurements, the value being strongly dependent on the composition. A significant contribution of the extrinsic effect to elastic, dielectric and electromechanical properties is revealed for MPB BNT-xBT. The Bi3+ substitution by Ba2+ leads to the formation of A-site vacancies, which give rise to the enhancement of domain wall motion, as occurs in other perovskite-type piezoelectrics. Good functional properties are achieved for x = 0.07 (d33 = 180 pC/N), which are similar or even better than those obtained by complex synthesis routes. This system exhibits a remarkable stability in the permittivity that has hitherto not been reported. This fact may open the way for BNT-BT compositions to be used in specific applications in which lead-free piezoceramics have previously been employed with little success, e.g. in high power devices.