The move by the U.S. Judicial Conference comes after high-profile cases in which lawyers have effectively been able to pick the judge.

When anti-abortion activists drafted a lawsuit seeking to overturn federal approval of the abortion pill mifepristone, they filed it in a court in Texas where they were guaranteed a judge who they thought would be friendly to their point of view.

That judge, Amarillo-based Matthew Kacsmaryk who was once a conservative legal activist and was appointed by former President Donald Trump, subsequently ruled in favor of the plaintiffs, prompting outcry and further litigation. The case is now before the Supreme Court.

The approach that the lawyers at the Christian conservative Alliance Defending Freedom took in that case, known as “judge-shopping,” will be harder to pull off following a policy change made Tuesday by the federal judiciary.

The U.S. Judicial Conference at its biannual meeting approved a new policy that would ensure that any cases seeking to block state or federal policies in federal district courts would be assigned randomly from a larger pool of judges.