The back-reflect ion double-scanning diffractometer method, by which lattice parameters can be measured with a reproducibility of one part in 150,000 has been applied at liquid helium temperatures. A cryostat attachment is described which enables diffraction profiles to be scanned on both sides of the primary X-ray beam up to 163°, 2θ. Alignment errors may, thus, be eliminated by measuring the included angle 4θ between respective Bragg reflections. The method is illustrated by measuring the lattice parameters of the I.U.Cr. standard specimens of silicon and tungsten at various cryogenic temperatures.