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Motivated by the Markov chain Monte Carlo (MCMC) relaxation method of Jalali and Weissman, we propose a lossy compression algorithm for continuous amplitude sources that relies on a finite reproduction alphabet that grows with the input length. Our algorithm asymptotically achieves the optimum rate distortion (RD) function universally for stationary ergodic continuous amplitude sources. However, the large alphabet slows down the convergence to the RD function, and is thus an impediment in practice. We thus propose an MCMC-based algorithm that uses a (smaller) adaptive reproduction alphabet. In addition to computational advantages, the reduced alphabet accelerates convergence to the RD function, and is thus more suitable in practice.