The prevalence of fetal chromosome anomalies rises exponentially with the age of the pregnant woman. The risk of fetal anomalies can be specified using biochemical screening tests such as the triple test. This test substantially reduces the number of amniocenteses and proportionally the number of procedure-related miscarriages. However, disadvantages of the triple test include the utility loss of pregnant women who, following a false-negative test result, do not undergo amniocentesis and bear a disabled child as well as the intangible cost of a false-positive triple test. This paper employs a decision-analytic model to reveal the evaluation of this tradeoff, which is implicitly fixed by policy recommendations for a direct amniocentesis at maternal age of 35. It then determines the optimal level of cutoff risk for the triple test, and derives comparative static results: the optimal test accuracy decreases with increasing a-priori risk and increases with a rise in the miscarriage risk and in the woman's preference for detecting an affected fetus as compared to avoiding a miscarriage of an unaffected fetus. These results are in contrast to current clinical practice, where the cutoff of the triple test usually remains fixed.