Several states with near-total abortion bans have introduced legislation seeking to make their medical exceptions clearer.

A bill that clarifies the medical exceptions to the state of Texas' near-abortion ban could be headed to the governor's desk as early as Thursday. It comes as lawmakers in the Texas House gave preliminary passage of the legislation Wednesday afternoon.

That bill passed the Texas Senate in mid-April. An amended version passed the Texas House, with a narrower margin than the abortion clarification bill. The clarification legislation received widespread support from a variety of lawmakers and advocacy groups, to a degree that’s unusual for an abortion-related bill.