We study the growth (‘‘coarsening’’) of domains following a quench in an Ising model with weak next‐nearest‐neighbor antiferromagnetic (AFM) bonds and single‐spin‐flip dynamics. The AFM bonds introduce free energy barriers to coarsening and thus greatly slow the dynamics. In three dimensions, simple physical arguments suggest that the barriers are proportional to the characteristic length scaleL(t) for quenches below the corner rounding transition temperatureTCR. This should leadL(t)∼log(t) at long timest. Monte Carlo simulations provide strong support for this claim.We also predict logarithmic growth in a purely two‐dimensional tiling model, which can be thought of as describing a single interface in our three‐dimensional model viewed from the direction. Here, the slow coarsening dynamics should persist all the way up to the order‐disorder transition (atTCR). However, if the model is cooled slowly at a rate &Ggr;, the final length scale should have power‐law, not logarithmic, dependence of 1/&Ggr;. Simulations support both of these claims.