The two-dimensional Ising model with Brascamp-Kunz boundary conditions
has a partition function more amenable to analysis
than its counterpart on a torus. This fact is exploited
to *exactly* determine the full finite-size scaling behaviour
of the Fisher zeroes of the model. Moreover, exact results are also
determined for the scaling of the specific heat at criticality,
for the specific-heat peak and for the
pseudocritical points. All corrections to scaling are found
to be analytic and the shift exponent lambda does not coincide
with the inverse of the correlation length exponent 1/nu.