A few years ago, a law was passed in Israel, allowing couples to apply for permission to use PGD (pre-implantation genetic diagnosis, a method in which genetic testing is done on an embryo prior to transferring it to the uterus) in order to select a specific gender. The criteria included having 4 or more children of the same gender and that having an additional child of the same gender would put significant stress either on the parents or on the child who was born. A panel that includes doctors, a psychologist, a person representing religious aspects, etc. meet with the couple to hear their story and make the decision.
I just read this article (using the translate function works OK, not great)... and found this part fascinating (adapted from the Google translation): In some cases, the committee has approved ultra-Orthodox religious families' choice to have a daughter. This is in cases in which the family is either Cohen or Levi and the couple requires sperm donation in order to have a child. In this case, the parents are concerned that once the child reaches the age of bar mitzvah, they will not be able to let him have an aliyah* as a Cohen or Levi & will have to disclose the fact that he was born as a result of sperm donation to the community. These couples would rather have no children than risk the birth of a son... There's still one issue that it doesn't solve - that of a Pidyon HaBen - because a daughter of a Cohen wouldn't have to have one for her son... (so a girl born as a result of sperm donation would be required to have a Pidyon HaBen for her son, but wouldn't know that she should.) I wonder how they solve that problem - especially since that too is a public ceremony. Perhaps they spend the first 20 years of her life praying that her firstborn is a girl**...
*Aliyah - the honor of being called up to participate in the reading of the Torah in the synagogue
**By age 20, many ultra-Orthodox girls are married and become mothers
Dee updated: Dee's RE called today to say that in addition to the 2 embryos they transferred, they've got an amazing blastocyst that they just have to transfer too. (I've never heard of two transfers during the same cycle - must be something more recent than my experience.) I don't know what her choice will be... (I think I would have gone for it :-))