Extraordinary magnetostrictive behavior has been observed in Fe-Ga alloys with concentrations of Ga between 4% and 27%. λ₁₀₀ exhibits two peaks as a function of Ga content. At room temperature, λ₁₀₀ reaches a maximum of 265 ppm near 19% Ga and 235 ppm near 27% Ga. For compositions between 19% and 27%, λ₁₀₀ drops sharply to a minimum near 24% Ga and exhibits an anomalous temperature dependence, decreasing by as much as a factor of 2 at low temperatures. This unusual magnetostrictive behavior is interpreted on the basis of a single maximum in the magnetoelastic coupling ∣b₁∣ of Fe with increasing amounts of nonmagnetic Ga, combined with a strongly temperature dependent elastic shear modulus (c₁₁−c₁₂) which approaches zero near 27% Ga. λ₁₁₁ is significantly smaller in magnitude than λ₁₀₀ over this composition range, and has an abrupt change in sign from negative for low Ga concentrations to positive for a concentration of Ga near 21%.