We have re-analysed the relationships between velocity dispersion, line strength and absolute magnitude for normal elliptical galaxies. We find that, at fixed absolute magnitude, galaxies with high velocity-dispersions tend to have high line-strengths and those with low velocity-dispersions have low line-strengths. This implies that elliptical galaxies are at least a two-parameter family. This conclusion is based on a preliminary sample of 24 galaxies for which both types of measurements are available. Well-known apparent scale differences in velocity dispersion between various authors are shown to be due to mean line-strength differences between galaxy samples. After correction for this effect, all sources considered here agree well to within a few per cent. The present data also suggest that the velocity-dispersion and line-strength residuals may in turn be correlated with intrinsic axial ratio, with flatter ellipticals having smaller velocity dispersions and metallicities. The correlation between residual metallicity and axial ratio is of special importance since measured metallicity is independent of aspect angle. If this relation holds up on tests with larger samples, it could offer a number of new ways to determine the true figures and axial ratios of elliptical galaxies. These new results are discussed in the context of dissipational and dissipationless collapse models for elliptical galaxy formation. They indicate a strong link between the dynamical and chemical evolutions of elliptical galaxies which seems quite compatible with the dissipational picture, where stars formed during the collapse phase at the same time as the final dynamical characteristics of the galaxy were determined. Merger models involving largely gaseous fragments also appear viable. By contrast, purely stellar collapses or mergers would seem to require additional, somewhat ad hoc assumptions. The interpretation of the systematically bluer colours of cD galaxies may be complicated by their tendency to be flatter than normal ellipticals.