Twin births are an important instrumental variable for the endogenous fertility decision. However, in many economic settings, twins are not exogenous as dizygotic twinning is known to be correlated with maternal characteristics and fertility treatments. Following the medical literature, we assume that monozygotic twins are exogenous, and construct a new instrument, which corrects for the selection bias although monozygotic twinning is usually unobserved. We use longitudinal administrative data from Sweden and US census data and show that the usual twin instrument is not only related to observed but also to unobserved determinants of economic outcomes, while our new instrument is not. We demonstrate the relevance of our new instrument in two labor market applications and find that the classical twin instrument underestimates the true negative effect of fertility on labor force participation and earnings.