Throughout the years spanned by the U.S. Vital Statistics Linked Birth and Infant Death Data (1983-2002), 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. This has crucial implications for any study using a regression discontinuity design in which birth weights are used as the running variable. For example, estimates will be biased in a manner that leads one to conclude that it is “good” to be strictly to the left of 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. This analysis highlights a more general problem that can afflict regression discontinuity designs. In cases where attributes related to the outcomes of interest predict heaping in the running variable, estimated effects are likely to be biased. We discuss approaches to diagnosing and correcting for this type of problem.