  The configurational entropy of ice is calculated by thermodynamic integration
from high to low temperatures. We use Monte Carlo simulations with a simple
energy model which reproduces the Bernal-Fowler ice rules. This procedure is
found to be precise enough to give reliable values for the residual entropy
s_th of different ice phases in the thermodynamic limit. First, we check it for
a two-dimensional ice model. Second, we calculate s_th for ice Ih, and compare
our result with those previously given in the literature. Third, we obtain s_th
for ice VI, for which we find a value clearly higher than for ice Ih.
