Antenatal screening for fetal anomalies has provided women and their partners with information to make reproductive choices based on the risk of serious chromosomal or structural defects since the 1990s. Alternative tests include first‐trimester screening (combined ultrasound and maternal serum markers), second‐trimester maternal serum markers and noninvasive cell‐free DNA testing. The recent recommendations by the Royal Australian and New Zealand College of Obstetrics and Gynaecology and the Human Genetics Society of Australasia against second‐trimester triple testing are based on unsound performance criteria, raise several contestable issues around access and equity and challenge the principles of governments providing affordable options.