Background Customized fetal growth charts assume birthweight at term to be normally distributed across the population with a constant coefficient of variation at earlier gestational ages. Thus, standard deviation used for computing percentiles (e.g., 10^th, 90^th) is assumed to be proportional to the customized mean, although this assumption has never been formally tested. Methods In a secondary analysis of NICHD Fetal Growth Studies-Singletons (12 U.S. sites, 2009–2013) using longitudinal sonographic biometric data (n = 2288 pregnancies), we investigated the assumptions of normality and constant coefficient of variation by examining behavior of the mean and standard deviation, computed following the Gardosi method. We then created a more flexible model that customizes both mean and standard deviation using heteroscedastic regression and calculated customized percentiles directly using quantile regression, with an application in a separate study of 102, 012 deliveries, 37–41 weeks. Results Analysis of term optimal birthweight challenged assumptions of proportionality and that values were normally distributed: at different mean birthweight values, standard deviation did not change linearly with mean birthweight and the percentile computed with the normality assumption deviated from empirical percentiles. Composite neonatal morbidity and mortality rates in relation to birthweight < 10^th were higher for heteroscedastic and quantile models (10.3% and 10.0%, respectively) than the Gardosi model (7.2%), although prediction performance was similar among all three (c-statistic 0.52–0.53). Conclusions Our findings question normality and constant coefficient of variation assumptions of the Gardosi customization method. A heteroscedastic model captures unstable variance in customization characteristics which may improve detection of abnormal growth percentiles. Trial registration ClinicalTrials.gov identifier: NCT00912132.