This study demonstrates that regression discontinuity designs will arrive at biased estimates when attributes related to outcomes predict heaping in the running variable. We discuss several approaches to diagnosing and correcting for this type of problem. Our primary example focuses on the use of birth weights as a running variable. We begin by showing that birth weights are measured most precisely for children of white and highly educated mothers. As a result, less healthy children, who are more likely to be of low socioeconomic status, are disproportionately represented at multiples of round numbers. For this reason, RD estimates using birth weight as the running variable will be biased in a manner that leads one to conclude that it is "good" to be strictly less than any 100-gram cutoff. As such, prior estimates of the effects of very low birth weight classification (Almond, Doyle, Kowalski, and Williams 2010) have been overstated and appear to be zero. We also demonstrate potential problems using days of birth or grade point averages as running variables.