Twin births are often construed as a natural experiment in the social and natural sciences on the premise that the occurrence of twins is quasi-random. We present new population-level evidence that challenges this premise. Using individual data for more than 18 million births (more than 500,000 of which are twins) in 72 countries, we demonstrate that indicators of the mother's health and health-related behaviours and exposures are systematically positively associated with the probability of a twin birth. The estimated associations are sizeable, evident in richer and poorer countries, and evident even in a sample of women who do not use IVF. The positive selection of women into twinning implies that estimates of impacts of fertility on parental investments and on women's labour supply that use twin births to instrument fertility will tend to be downward biased. This is pertinent given the emerging consensus that these relationships are weak. Using two large samples, one for developing countries and one for the United States, and focusing upon twin-instrumented estimates of the quantity–quality trade-off, we demonstrate the nature of the bias and estimate bounds on the true parameter.