This article is from the Pregnancy Screening FAQ, by Lynn Gazis-Sax (firstname.lastname@example.org) with numerous contributions by others.
Amniocentesis is recommended when the risk of a disability detectable
by amnio is judged to be greater than the risk from amniocentesis.
People for whom amniocentesis is likely to be recommended include:
women with an abnormal result on the AFP or Down's screen which is not
explained by ultrasound (indicating, depending on the result, either
increased risk of Down syndrome or increased risk of neural tube
defects), women with a previous child with a disability which amnio
can detect (in whom it is unreasonable to do a Down's screen because
their prior risk is so high that the Down's screen should not alter
the Obstetrician's action), women who have had three or more
miscarriages (this one is questionable because amnio can cause
miscarriage and in many cases of recurrent abortion a cause is not
known), carriers for conditions (such as Tay Sachs) which can be
detected, carriers of sex-linked conditions such as hemophilia,
pregnancies in which one of the parents is known to have rearranged
chromosomes, women with ultrasound results showing a fetal anomaly
compatible with a chromosomal abnormality, and advanced age.
The most common reasons for having an amnio recommended are AFP results
and age. The reason for giving amnios to older women is that chromosomal
abnormalities (mainly Down syndrome, but also other trisomies) are more
common in older women. When amniocentesis was first available, it was
recommended for women over 40. As it has become more available, the age
at which it is recommended has been lowered, and it is now often offered
to all pregnant women over the age of 35.