The Ising model in two dimensions with the special boundary conditions of Brascamp and Kunz is analysed. Leading and sub-dominant scaling behaviour of the Fisher zeroes are determined exactly. The finite-size scaling, with corrections, of the specific heat is determined both at the critical and pseudocritical points. The shift exponents associated with scaling of the pseudocritical points are not the same as the inverse correlation length critical exponent. All corrections to scaling are analytic.