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Simple acceptance/rejection has been a valuable tool for over half a century for obtaining variates from distributions with unknown normalizing constants. Unfortunately their performance typically degrades exponentially in the size of the problem. I will look here at three methods that solve this difficulty for three different problems. First I will examine generating variates from the tails of sums of random variables, then look at generating perfect matchings of regular graphs, and finally employ the Randomness Recycler method on the Ising model.