A class of optimal transformations is defined through the weight function which, when implemented into simple approximations of the renormalisation group, predicts values for the thermal exponent, yT, and the magnetic field exponent, yH, which are in better agreement with the exact results than those obtained with the majority sign rule. Specifically, the authors find that for the ferromagnetic triangular Ising lattice yT=0.914 and yH=1.908 (using the same approximation, the majority sign rule predicts yT=0.736 and yH=1.669). This weight function is used to calculate the properties of the ferromagnetic and antiferromagnetic square Ising lattice with a two-cell cluster and a one-hypercube approximation. The weight function is the first stage in the development of a real-space renormalisation group transformation free of the 'peculiarities' observed by Griffiths (1981).