Improved analytical representations of X-ray atomic form factors are put forward based on the inverse Mott–Bethe formula. Applying these representations, the mean absolute errors calculated for the complete set of form factors given in Table 6.1.1.1 inInternational Tables for Crystallography, Vol. C, 3rd ed., are reduced by a factor of ∼50 from previous published analyses. Various form factor compilations are examined to record the applicability of the approach outlined.