  Saturation field entropies of antiferromagnetic Ising models on quasi
one-dimensional lattices (ladders) and the kagome lattice are calculated. The
former is evaluated exactly by constructing the corresponding transfer
matrices, while the latter calculation uses Binder's algorithm for efficiently
and exactly computing the partition function of over 1300 spins to give, in
Boltzmann's units, S = 0.393589(6). We comment on the relation of the kagome
lattice to the experimental situation in the spin-ice compound dysprosium
titanium oxide.
