In a recent note Barber showed, for a spin-1/2 Ising system with ferromagnetic pair interactions, that some critical exponents of the triplet order parameter i j k are the same as those of the magnetization i . Here we prove such results for all odd correlations and dispense with the requirement of pair interactions. We also prove that the critical temperatureT c , defined as the temperature below which there is a spontaneous magnetization, is for fixed even spin interactionsJ e independent of the way in which the odd interactionsJ o approach zero from above. This is achieved by using only the simplest, Griffiths-Kelley-Sherman (GKS), inequalities, which apply to the most general many-spin, ferromagnetic interactions.