With gloved hands, a person inserts a liquid into a petri dish.

Britain is about to become the only country in the world to explicitly allow the inheritable genetic modification of humans. With a vote Feb. 3 in the House of Commons, the country has paved the way for "three-person in vitro fertilization," which combines genetic material from two women and a man.

Creating high-tech procedures like this to help women have healthy babies seems worthy of unquestioning support. But it's not so simple — and promises to soon get more complicated.

The techniques at immediate issue are relatively crude. They work by removing the nucleus from the egg (or embryo) of an intended mother, and inserting it into one provided by a second woman. Any resulting child would inherit its nuclear DNA from the intended mother and father and its mitochondrial DNA from the second woman.

Mitochondria exist inside cells, but outside the nucleus, and are passed from mother to child. The aim of the procedure is to prevent the transmission of defective mitochondrial genes that cause diseases.

There are a wide variety of mitochondrial diseases, and most also involve genetic...