The non-linear portion of the calibration graphs in flame atomic-absorption spectrometry (AAS) offers more precise analytical results provided that the calibration graph can be determined reliably. Experimental data for three elements (Cu, Ni, Pb) and synthetic data were submitted to nine analysts and to three mathematical expressions (polynomial, cubic spline and rational function). The quality of hand-drawn and computer-calculated graphs was judged for goodness of fit and the accuracy of determining unknowns. It is concluded that results within 1% can be obtained in either instance, provided that 5–8 selected reference solutions are used and weighting factors are applied in the least-squares fit. With a simple criterion to guide the selection of the correct degree, the ordinary polynomial is the preferred expression to fit flame AAS data. With these recommendations it is possible to extend the calibration graph at least to the point where the slope is reduced to 25% of its value at the origin.