Modulation‐doped In 0.3 Ga 0.7 As/In 0.29 Al 0.71 As heterostructures have been grown on GaAs substrates by molecular beam epitaxy using a compositionally step‐graded In x Ga 1-x As buffer layer. We found that the buffer layer produces essentially total relaxation with ≪2×10⁶/cm² dislocations present in the In 0.3 Ga 0.7 As layer. The structural perfection of this layer is reflected in the electrical and galvanomagnetic properties of its two‐dimensional electron‐gas channel which has a sheet‐electron density of 1.2×10¹²/cm², peak mobilities of 9 300 cm²/V s at room temperature and 31 000 cm²/V s at 77 K, and a mobility anisotropy of ∼4% along orthogonal 〈110〉 directions.