  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 $1/\nu$.
