Full-matrix least-squares is taken as the basis for an examination of protein-structure precision. A two-atom model is used to compare the precisions of unrestrained and restrained refinements. In this model, restrained refinement determines a bond length which is the weighted mean of the unrestrained diffraction-only length and the geometric-dictionary length. As a protein example, data with 0.94 Å resolution for concanavalin A are used in unrestrained and restrained full-matrix inversions to provide e.s.d.'s σ(r) for positions and σ(l) for bond lengths. σ(r) is as small as 0.01 Å for atoms with low Debye B values but increases strongly with B. The results emphasize the distinction between unrestrained and restrained refinements and also between σ(r) and σ(l). An unrestrained full-matrix inversion for an immunoglobulin with 1.7 Å data is also discussed. Several approximate methods are examined critically. These include Luzzati plots and the diffraction-component precision index (DPI). The DPI estimate of σ(r, B_avg) is given by a simple formula, which uses R or R_free and is based on a very rough approximation to the least-squares method. Examples show its usefulness as a precision comparator for high- and low-resolution structures.