The birth weight-specific mortality curves for exposed and unexposed populations (e.g., smokers vs non-smokers) cross so that low birth weight (LBW) babies in exposed populations have a lower neonatal mortality than LBW babies in unexposed populations. There are competing statistical and biologic theories to explain this birth weight “paradox”. The authors used causal diagrams to show that the “paradox” can be conceptualized as selection bias due to stratification on a variable (birth weight) that is affected by the exposure of interest (e.g., smoking), and shares common causes with the outcome (infant mortality). 1991 U.S. Birth data was used to illustrate how crossing of birth-weight specific mortality curves is the expected result of the causal links between risk factors, birth weight and neonatal mortality. For example, the authors estimated the total effect of smoking on neonatal mortality without conditioning on any intermediate variable (relative risk: 1.5). After conditioning on LBW, as is usually done in an attempt to assess the direct effect of smoking not mediated through LBW, and found an inverse association (relative risk: 0.9) between smoking and mortality among LBW infants. This birth weight “paradox” has been extensively studied, and several statistical and biologic theories have been proposed to explain it. A method based on comparing the birth weight Z-scores, rather than the birth weights, between the exposed and the unexposed has been proposed as a strategy to eliminate the “paradox”. We have argued elsewhere that the “paradox” is an example of selection bias due to adjustment for birth weight, a variable affected by the exposure. We show here that the Z-score method can be seen as a sophisticated version of not adjusting for birth weight. This claim is illustrated by applying the Zscore method to real data and to data sets simulated under several states of nature represented by different causal diagrams (directed acyclic graphs). For example, under the null hypothesis (exposure-mortality crude odds ratio equal to 1), the Z-score adjusted odds ratio is also one even though the birth weight-adjusted odds ratio can be arbitrarily far from 1. The need for a clear specification of the causal question that motivates the data analysis is reiterated.