I shift, stretch, and transform the observed cohort age-schedule of first birth for Danish women born in 1963 to see how late the mean age at first birth could plausibly shift. Constraints of two kinds are placed on the ultimate distribution of first births. First, no more than one-third of first births can occur after age 35. This constraint allows postponement without radical changes in childlessness or parity distribution. Second, I preserve some variability in the age at first birth by keeping the standard deviation of first birth above 4 years, the minimum value observed for Denmark during the baby boom years. Under these constraints, I find that mean ages at first birth of at least 33 years are plausible. This would represent a further increase of about 4 years in the mean age at first birth seen in recent periods. I conclude that the depressed levels of fertility seen due to postponement could continue for decades before limits are reached.