A scanning range over Bragg angles from −163 to +163° 2θ is obtained by combining a diffractometer capable of scanning both sides of the primary X-ray beam with a very short (3-in.) high-power focused X-ray tube. The ability to scan the included angle 4θ between respective diffraction profiles on either side of the primary beam over the entire range of Bragg angles, provides a direct method of eliminating errors caused by a displacement of the specimen surface from the axis of the goniometer. The method is demonstrated by determining the lattice parameters of standard specimens used in the I.U.Cr. Precision Lattice Parameter Project.