Many long-distance phonological processes exhibit what I call distance-based decay: the likelihood of application decreases as transparent distance increases. This article provides a robust model of distance-based decay within Maximum Entropy Harmonic Grammar (Smolensky 1986, Goldwater and Johnson 2003), drawing from thousands of data reflecting three processes across four languages. I reject using distance-specific constraints, and instead posit a decay function that scales the weight of a single AGREE/DISAGREE constraint with increasing distance (Kimper 2011). Though decay rates differ empirically across the four languages, I capture such differences purely with the weight of markedness and the weight of faithfulness without having to fit the decay function to each language. I argue based on statistical measures that distance is best measured in syllables rather than segments, supporting Martin 2005. The decay function takes as input a modified version of syllable count and returns a value that is then multiplied by the weight of AGREE/DISAGREE. It takes the form of a negative power function, which I show performs better than a down-sloping linear function.