The width of the wetted region at coherent twin boundaries in L12-ordered Cu-17% Pd has been determined at a set of accurately defined temperatures close to the critical temperatureTc. Analysis of the data shows a significant deviation from a logarithmic divergence of the width very close toTcas previously determined for antiphase boundaries in the same alloy by Ricolleauet al. It is shown that the fluctuations in width may give a consistent description of these deviations.