The variance of the pair correlation function, the tripler correlation function, g((3))(r, s, t), and the three-body contribution to the configurational entropy, S-3, were studied as possible tools for distinguishing between three different models of amorphous silicon (a-Si) with (nearly) identical pair correlation functions. All of these quantities were shown to be able to make the distinction unequivocally. For practical reasons, short-range S-3 is suggested as the best quantitative measure of disorder, in terms of higher-order correlations. For the first time, various projections of the three-body correlation function of a complicated amorphous material are also shown. On the basis of the current study it is proposed that the most realistic structural model of a-Si is the reverse Monte Carlo fit, starting from the well known Wooten model.