The Bond method for accurate lattice‐parameter measurements has been applied to spheroidal crystals smaller in diameter than the incident beam. By measuring bothhand to reduce the effects of mis‐centering and using a circle accurate to ±0.001°, a precision of a few parts per million can be attained. The accuracy of the method has been tested by measuring the lattice parameter of vacuum float‐zone refined silicon by the conventional Bond method (using large, flat specimens) and by the modified method (using spheroidal specimens 0.25 mm in diameter). The results indicate that in addition to the usual corrections for refraction, emission‐line asymmetry, and vertical divergence, a correction is required for changes in the asymmetric diffraction profile caused by the combined effects of horizontal divergence and absorption in the sphere. The correction is approximately 15 p.p.m. or 0.000079 Å in the case of the Si spheres and an instrument having a horizontal divergence of ±0.0013 rad. The corrected lattice parameter agrees within 4 p.p.m. with results obtained by the conventional method. These results demonstrate the feasibility of making precise and accurate measurements on many materials that are not available in the form of larg