We study the concentration of a degree- polynomial of the spins of a general Ising model, in the regime where single-site Glauber dynamics is contracting. For , Gaussian concentration was shown by Marton (1996) and Samson (2000) as a special case of concentration for convex Lipschitz functions, and extended to a variety of related settings by e.g., Chazottes et al. (2007) and Kontorovich and Ramanan (2008). For , exponential concentration was shown by Marton (2003) on lattices. We treat a general fixed degree with coefficients, and show that the polynomial has variance and, after rescaling it by , its tail probabilities decay as for deviations of .