Lawyers for the same-sex Arkansas couples who won the right to list both spouses on birth certificates of their newborn children are back before the U.S. Supreme Court, seeking attorney fees the Arkansas Supreme Court has denied.

Douglas Hallward-Driemeier, a partner at Ropes & Gray who won the 2017 case Pavan v. Smith, filed a cert petition this week asserting that lawyers for the couples are “indisputably prevailing parties within the meaning of the fee-shifting provision” of federal law and should be awarded an estimated $220,000 in legal fees.