  We report tests of finite-size scaling ansatzes in the low temperature phase
of the two-dimensional Ising model. For moments of the magnetisation density,
we find good agreement with the new ansatz of Borgs and Koteck\'y, and clear
evi consequences of the convexity of the free energy are not adequately treated
in either of these approaches.\lb {\it Keywords}\/: Finite-size scaling, 2-d
Ising, pure-phase susceptibility.
