This paper demonstrates that the apparently much higher Hispanic/Mexican fertility is almost exclusively the product of period estimates obtained for immigrant women and that period measures of immigrant fertility suffer from 3 serious sources of biases that together significantly overstate fertility levels: difficulties in estimating the size of immigrant groups; the tendency for migration to occur at a particular stage in life; and most importantly the tendency for women to have a birth soon after migration. Once these sources of bias are taken into consideration the fertility of native Hispanic/Mexican women is very close to replacement level. In addition, the completed fertility of immigrant women in the United States is dramatically lower than the level obtained from period calculations. Findings are consistent with classical theories of immigrant assimilation but are a striking departure from the patterns found in previous studies and published statistics. The main implication is that, without a significant change in immigration levels, current projections based on the premise of high Hispanic fertility are likely to considerably exaggerate Hispanic population growth, its impact on the ethno-racial profile of the country, and its potential to counteract population aging.