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We present a strategy for the design of ferromagnetic materials with exceptionally low magnetic hysteresis, quantified by coercivity. In this strategy, we use a micromagnetic algorithm that we have developed in previous research and which has been validated by its success in solving the “Permalloy Problem”—the well-known difficulty of predicting the composition 78.5% Ni of the lowest coercivity in the Fe–Ni system—and by the insight it provides into the “Coercivity Paradox” of W. F. Brown. Unexpectedly, the design strategy predicts that cubic materials with large saturation magnetizationm_sand large magnetocrystalline anisotropy constantκ₁will have low coercivity on the order of that of Permalloy, as long as the magnetostriction constantsλ₁₀₀, λ₁₁₁are tuned to special values. The explicit prediction for a cubic material with low coercivity is the dimensionless number$$({c}_{11}-{c}_{12}){\lambda }_{100}^{2}/(2{\kappa }_{1})=81$$$\left(c_{11}-c_{12}\right){\lambda }_{100}^2/\left(2{\kappa }_1\right)=81$for 〈100〉 easy axes. The results would seem to have broad potential application, especially to magnetic materials of interest in energy research.