The semi-empirical mass formula of Bethe and von Weizsäcker is extended to include a number of additional terms. All possible combinations of extra terms are fitted in turn to the measured nuclear masses and the results analysed in order to reveal correlations and mutual influences between the various terms. The surface symmetry term is shown to be of critical importance in determining the Wigner and symmetry coefficients, while the pairing and global shell correction terms are largely independent of the other terms in the formula. The curvature term has a strong effect on the values of the other fit parameters. The interplay between different terms is found to be important. Some of the coefficients turn out to be much more poorly determined than would be suggested by standard fit errors alone.