Piezoelectric actuators transform electrical energy into mechanical energy, and because of their compactness, quick response time and accurate displacement, they are sought after in many applications. Polycrystalline piezoelectric ceramics are technologically more appealing than single crystals due to their simpler and less expensive processing, but have yet to display electrostrain values that exceed 1%. Here we report a material design strategy wherein the efficient switching of ferroelectric-ferroelastic domains by an electric field is exploited to achieve a high electrostrain value of 1.3% in a pseudo-ternary ferroelectric alloy system, BiFeO3-PbTiO3-LaFeO3. Detailed structural investigations reveal that this electrostrain is associated with a combination of several factors: a large spontaneous lattice strain of the piezoelectric phase, domain miniaturization, a low-symmetry ferroelectric phase and a very large reverse switching of the non-180 degrees domains. This insight for the design of a new class of polycrystalline piezoceramics with high electrostrains may be useful to develop alternatives to costly single-crystal actuators.