Are attempts to have impaired children justifiable?

In a recent case, artificial insemination was employed by a couple in an attempt to ensure the birth of a deaf child. In response to this, I argue that individuals should not be allowed to select for or against deafness. While I establish that preferences for deaf children can be inherently just, allowing individuals to secure these preferences may have unacceptable consequences for existing persons who are deaf. I show that these follow even granting this couple's contestable understanding of the deaf as a minority group.