Rejection sampling is a common tool for low dimensional problems (d ≤ 2), often touted as an “easy” way to obtain valid samples from a distribution f(·) of interest. In practice it is non-trivial to apply, often requiring considerable mathematical effort to devise a good proposal distribution g(·) and select a supremum C. More advanced samplers require additional mathematical derivations, limitations on f(·), or even cross-validation, making them difficult to apply. We devise a new approximate baseline approach to rejection sampling that works with less information, requiring only a differentiable f(·) be specified, making it easier to use. We propose a new approach to rejection sampling by refining a parameterized proposal distribution with a loss derived from the acceptance threshold. In this manner we obtain comparable or better acceptance rates on current benchmarks by up to 7.3×, while requiring no extra assumptions or any derivations to use: only a differentiable f(·) is required. While approximate, the results are correct with high probability, and in all tests pass a distributional check. This makes our approach easy to use, reproduce, and efficacious.