We present efmaral, a new system for efficient and accurate word alignment using a Bayesian model with Markov Chain Monte Carlo (MCMC) inference. Through careful selection of data structures and model architecture we are able to surpass the fast_align system, commonly used for performance-critical word alignment, both in computational efficiency and alignment accuracy. Our evaluation shows that a phrase-based statistical machine translation (SMT) system produces translations of higher quality when using word alignments from efmaral than from fast_align, and that translation quality is on par with what is obtained using giza++, a tool requiring orders of magnitude more processing time. More generally we hope to convince the reader that Monte Carlo sampling, rather than being viewed as a slow method of last resort, should actually be the method of choice for the SMT practitioner and others interested in word alignment.