Low birth weight (LBW) infants have lower infant mortality in groups in which LBW is most frequent. For example, in 1991, US infants born to smokers had higher risks of both LBW and infant mortality than infants born to nonsmokers. However, among LBW infants, infant mortality was lower for infants born to smokers (relative rate = 0.79). There are competing theories regarding this so-called "paradox." One is that maternal smoking is beneficial for LBW infants. The authors use causal diagrams to show that, even in the absence of any beneficial effect of smoking, an inverse association due to stratification on birth weight can be found. This variable is affected by the exposure of interest and shares common causes with the outcome. That is, LBW infants born to smokers may have a lower risk of mortality than other LBW infants whose LBW is due to causes associated with high mortality (e.g., birth defects). Under realistic causal diagrams, adjustment for birth weight is unwarranted when the analytical goal is to estimate overall effects of prenatal variables on infant mortality. Even for estimating direct effects of prenatal variables, adjustment for birth weight may be invalid when there is an unmeasured common cause of LBW and mortality. An appropriate justification for conditioning on birth weight requires specifying 1) the causal question motivating this analytical approach and 2) the assumptions regarding the proposed underlying biologic mechanisms.