accelerating MCMC

I have recently [well, not so recently!] been asked to write a review paper on ways of accelerating MCMC algorithms for the [review] journal WIREs Computational Statistics and would welcome all suggestions towards the goal of accelerating MCMC algorithms. Besides [and including more on]

• coupling strategies using different kernels and switching between them;
• tempering strategies using flatter or lower dimensional targets as intermediary steps, e.g., à la Neal;
• sequential Monte Carlo with particle systems targeting again flatter or lower dimensional targets and adapting proposals to this effect;
• Hamiltonian MCMC, again with connections to Radford (and more generally ways of avoiding rejections);
• adaptive MCMC, obviously;
• Rao-Blackwellisation, just as obviously (in the sense that increasing the precision in the resulting estimates means less simulations).