This time of year, some hospitals see a small uptick in baby deliveries thanks to families eager to fit the blessed event in around holiday plans or in time to claim a tax deduction. Conventional wisdom has long held that inducing labor or having a Caesarean section a bit early posed little risk, since after 34 weeks gestation, all the baby has to do was grow.

But new research shows that those last weeks of pregnancy are more important than once thought for brain, lung and liver development. And there may be lasting consequences...