Smoking during pregnancy can have significant adverse health effects for babies, yet many women smoke during pregnancy. In this paper, we examine whether state tobacco control policies lead to improved birth outcomes and to what extent the success of these policies depends on accumulated maternal human capital. We use data from the Pregnancy Risk Assessment Monitoring System in a time period when states significantly changed their tobacco control policies. Results show that the smoking policies are limited in their effectiveness. The largest improvements in birth outcomes from higher cigarette prices are among babies of women who have accumulated the least human capital.