  {}From a finite-size scaling (FSS) theory of cumulants of the order parameter
at phase coexistence points, we reconstruct the scaling of the moments.
Assuming that the cumulants allow a reconstruction of the free energy density
no better than as an asymptotic expansion, we find that FSS for moments of low
order is still complete. We suggest ways of using this theory for the analysis
of numerical simulations. We test these methods numerically through the scaling
of cumulants and moments of the magnetization in the low-temperature phase of
the two-dimensional Ising model. (LaTeX file; ps figures included as shar file)
