The location of x-ray diffractometer line profiles is of fundamental importance in x-ray stress analysis. Objective estimates of the line profile position may be derived from diffractometer measurements at a number of equally-spaced points in the region of maximum intensity. These estimates are generally based upon the corresponding turning-point of a polynomial fitted to step-scanning data. Techniques are described which simplify the computation involved. A least-squares fitting of a quadratic is satisfactory for most routine applications provided that a reasonable number of points is involved. The three-point parabola method is less satisfactory. Expressions are presented, derived using the maximum-likelihood approach, for peak location and counting variance using both quadratic and cubic equations.