Aims to improve the mixing rate of Gibbs sampling in pairwise Ising models with strong interactions, which are known to be "slow-mixing". Several projections to "fast-mixing" models are proposed; essentially, parameters are identified which are as close as possible to the original model, but weak enough to satisfy a spectral bound establishing rapid mixing. Experiments show some regimes where this leads to improved marginal estimates for a given computation time, compared to variational methods (mean field and belief propagation variants) and Gibbs sampling in the original model. The technical content builds heavily on prior results establishing conditions for rapid mixing [4,8]. But I haven't seen the idea of projecting onto the nearest rapidly mixing model, as an approximate inference method, explored before.