Previous analyses of prenatal screening for neural tube defects have generally found benefits to exceed costs. The usual screening battery follows an elevated maternal serum alpha-fetoprotein level with high-resolution ultrasound and/or amniocentesis. Current thinking focuses on weighing the risk of a false-negative (an abnormality missed) against the risk of an amniocentesis-induced fetal loss. This thinking neglects the risk of a false-positive (an unaffected fetus labeled abnormal) and individual parents' preferences concerning a false-negative vs a fetal loss. With these risks included, we find that high-resolution ultrasound is appropriate for all women with elevated serum alpha-fetoprotein. Women with moderately elevated serum alpha-fetoprotein who have negative ultrasound scans need no further testing, nor do women with highly elevated serum alpha-fetoprotein and positive ultrasound scans. Further testing using amniocentesis to confirm the ultrasound result is appropriate for women with moderately elevated serum alpha-fetoprotein and positive ultrasound scans, and for women with highly elevated serum alpha-fetoprotein and negative ultrasound scans. The actual cutoffs defining normal, moderately elevated, and highly elevated serum alpha-fetoprotein depend on several parameters, particularly the underlying prevalence of neural tube defects and the parents' preferences.