SHAKESPEARE, ALLOWING RICHARD III to explain the origins of his villainy, had him announce that he had been ''Deformed, unfinished, sent before my time/ Into this breathing world scarce half made up'' (Act I, Scene 1). What could be worse than a birth defect, what tragedy greater than a baby born abnormal?

So you want to have a baby. Naturally, a healthy baby, a perfect baby. You'll give up alcohol, drink your eight glasses of milk a day. You won't even take Tylenol. Maybe you'll finally go ahead and test your house for radon.

As medicine marches forward, one of the benefits we seek is certainty: give me the diet that will keep me healthy, the special bran muffin to lower my cholesterol. Do as many tests as you need, doctor, just make sure there's nothing wrong with me. And above all, promise me a healthy child. The astronomical rate at which obstetricians are sued by their patients reflects this; a good obstetrician is expected to deliver a perfect baby, and to foresee and circumvent any of the possible problems in pregnancy, labor and delivery.

In medicine in general, and in obstetrics in particular, this search for certainty leads to many invasive procedures. Now the search for a perfect baby is leading us further and further back into pregnancy, as the possibilities for prenatal diagnosis multiply.

Prenatal diagnosis starts before there is a fetus to diagnose. If two people are thinking of having a child together, they should give some thought to whether any genetic diseases run in their families, from the relatively common well-known disorders, such as hemophilia and muscular dystrophy, to such rare disorders as ceramidase deficiency and glycogen-storage disease. Any prospective parent whose family tree includes a number of childhood deaths, or a succession of congenital anomalies, should get genetic counseling promptly.

Even if there isn't any such family history, those who come from high-risk populations may want to be tested to see if they carry defective genes. Those with African ancestry can be tested for the sickle cell anemia gene; those with Eastern European Jewish forebears, for Tay-Sachs.

O.K., so now you're pregnant. And the obstetrician does the usual checkup on the fetus, listens to the heartbeat, measures the uterus - but what about the new, high-tech ways of making sure the baby is going to be all right?

The only prenatal screen routinely recommended for every pregnancy is an alpha-fetoprotein, or AFP, level. This is done on a small sample of the mother's blood, measuring a protein produced by the fetus. A protein level too low or too high for the stage of pregnancy prompts the doctor to do an ultrasound, using sound waves to create a picture of the fetus. Usually, it turns out that the estimated gestational age was wrong; ultrasound allows accurate dating of the pregnancy, and a high AFP level turns out to mean a baby due sooner than expected.

However, if the AFP is really too high, it raises the specter of congenital anomaly. AFP is elevated in spinal-cord defects, where the spinal column never fuses properly, causing spina bifida, for example. Other malformations that leave the internal organs exposed can also raise the AFP; such as gastroschesis, in which the intestines are outside the abdomen. Ultrasound detects most such major defects. But others - Turner syndrome, for example, a chromosomal abnormality in which a fetus has only one sex chromosome (a single X, instead of XX or XY) - cannot be diagnosed on ultrasound.

An AFP level that is too low is associated with Down's syndrome, as well as with another, more serious syndrome: trisomy 18. In trisomy 18, instead of the extra 21st chromosome seen in Down's, the fetus has an extra 18th chromosome; these babies will have multiple birth defects, and will not survive. These chromosomal syndromes really require amniocentesis for detection.

Although the American College of Obstetricians and Gynecologists does not actually recommend ultrasound as a routine test in a normal untroubled pregnancy, more and more doctors seem to be doing routine ultrasounds on more and more women. Some of this probably grows out of the parents' desire to be assured that all is well with the fetus; some grows out of the doctor's desire to guard against lawsuits by doing every test.

Ultrasound may or may not be accompanied by amniocentesis, in which a sample of amniotic fluid is withdrawn by needle, and the fetal cells are cultured and their chromosomes analyzed. This test is now recommended for women over the age of 35, a somewhat arbitrary number. As women age, the frequency of Down's syndrome in their offspring increases, and 35 marks the age at which this risk was thought to surpass the risk to the fetus from the procedure itself - there is a small incidence of miscarriage following amniocentesis. Now, women over 35 tend to have amniocentesis done, and the vast majority of babies with Down's syndrome are born to younger mothers; the younger group has a lower frequency of the defect, but a much higher birth rate, so the rare events add up.

Let me point out that morally we are already in deep weeds. Prenatal diagnosis, after all, carries with it the implication that, if an abnormality is found, the parents intend to consider the possibility of doing something about it, i.e., terminating the pregnancy. But the various abnormalities I have just listed constitute a wide spectrum. On one end, a trisomy 18, or a trisomy 13, is a fetus that many parents would choose to abort. If carried to term, these babies are profoundly abnormal, severely retarded, and tend to die soon. On the other hand, girls with Turner syndrome have only mildly unusual facial features, and grow up mentally normal. They suffer from certain medical problems - short stature and infertility, to name two - but they are by no means devastated.

Or take Down's syndrome, the reason for most over-35 amnios. Many women choose to abort fetuses with Down's - but I know parents who have raised children with the syndrome and are indignant at the idea of not allowing the birth of such babies, proud of their children's achievements. Such parents are quick to point out that their children are happy and loving.

Amniocentesis cannot be done until the second trimester, but the relatively new technique of chorionic villus sampling, or C.V.S., can sample fetal chromosomes as early as the ninth week.

Although geneticists can now ask a multitude of questions, the vast majority are not routinely broached with the average pregnancy. A 37-year-old woman has an amnio, and the fetal cells are checked for major chromosomal abnormalities, such as trisomys. However, without specific indications, no one looks at this DNA to find any other subtle genetic diseases. If there is a family history of cystic fibrosis, say, or of some enzyme deficiency, then that test is done, but most genetic diseases are so rare that it would make no sense to screen the general population.

The availability of these specific tests is a tremendous boon to families cursed with a deadly genetic disease. Consider Duchenne's muscular dystrophy, which is an X-linked disorder, a condition, like hemophilia, in which the mother is a carrier, with one normal X chromosome, and one that carries the muscular dystrophy. If her son inherits that one, he develops the disease and slowly loses his strength, ending up wheelchair-bound by 12 or 13, then losing the power of his respiratory muscles, and dying, usually of lung disease, often before the age of 20. Once, doctors told parents who were watching one well-loved son undergo this agony: next time have an amniocentesis, and if the fetus is male, consider abortion. There was no specific prenatal screen to tell whether a male had inherited the defective X. Now, the difficult decision of whether or not to carry a pregnancy to term can be fully informed. We can screen for muscular dystrophy.

BUT CERTAINTY cannot be bought. Geneticists caution that even if all the currently available genetic tests were done, they would not guarantee a perfect baby. Although we can test for a number of syndromes, which include mental retardation, these syndromes account for far fewer than half of the children diagnosed with mental retardation. Most have causes we cannot possibly pick up prenatally. And congenital anomalies occur more often than many people realize; by one recent estimate, one in every 50 babies has a defect, which vary in medical, cosmetic, or surgical significance. Most of these defects are not life-threatening, and even if we could detect them all prenatally, would we want to start terminating pregnancies for comparatively minor cardiac defects? Or for extra fingers and toes?

I believe that prospective parents are entitled to as much information as they feel they need, entitled to good genetic counseling, accurate testing and medical support for their decisions. I also believe they are entitled to do whatever they want with this information. I just think that before we reach out eagerly for all the new knowledge our expanding technology can offer, we need to stop and think about how we are going to use this information, how much of it we need, how much of it we want.

And as the technology for prenatal testing gets better and better, prospective parents will need to ask themselves some major questions: how, exactly, do they feel about abortion? How great is their need for a perfect child? And, if not a perfect child, how much imperfection can they tolerate - or love? How great a handicap would they want a child of theirs to bear? And we have to acknowledge that, for all of the technology, the growth of a fetus and the birth of a baby remain processes that are not completely under our control; perfect babies, in the end, are born, not made.