The magnetic shape-memory alloy Ni-Mn-Ga shows, in monocrystalline form, a reversible magnetic-field-induced strain (MFIS) up to 10%. This strain, which is produced by twin boundaries moving solely by internal stresses generated by magnetic anisotropy energy(1-4), can be used in actuators, sensors and energy-harvesting devices(5-7). Compared with monocrystalline Ni-Mn-Ga, fine-grained Ni-Mn-Ga is much easier to process but shows near-zero MFIS because twin boundary motion is inhibited by constraints imposed by grain boundaries(8-10). Recently, we showed that partial removal of these constraints, by introducing pores with sizes similar to grains, resulted in MFIS values of 0.12% in polycrystalline Ni-Mn-Ga foams(11), close to those of the best commercial magnetostrictive materials. Here, we demonstrate that introducing pores smaller than the grain size further reduces constraints and markedly increases MFIS to 2.0-8.7%. These strains, which remain stable over >200,000 cycles, are much larger than those of any polycrystalline, active material.