Mexican senators on Thursday overwhelmingly approved a sweeping judicial reform that would introduce public, oral trials and guarantee the presumption of innocence.

The Senate voted 71 to 25 in favor of the measure, after a clause that would have let police search homes without warrants was deleted from it.

The constitutional amendment, which must still be approved by at least 17 of Mexico’s 31 states, would replace closed-door proceedings in which judges rely on written evidence with U.S.-style open trials based on arguments presented by prosecutors and defense lawyers.

It would also allow recorded phone calls to be used as evidence in criminal cases if at least one of the conversation’s participants agrees.

Mexico’s lower house and Senate approved a version of the measure last year, but minor changes required new votes by both chambers. The Chamber of Deputies passed it in February by a 462-6 vote.

Several top law enforcement officials lamented the deletion of language in the original bill allowing warrantless searches of homes when police believe a life is in danger or a crime is being committed inside.

Prosecutors said such searches were necessary in cases where urgent action is needed to free kidnap victims. But it met with strong criticism from human rights groups, and legislators agreed to drop it.

The reform also creates a new class of judges to rule more quickly on warrant requests and provides a firmer legal footing for house arrest, which prosecutors often use to buy time to build a case against organized crime suspects.

Qualified public defenders will represent suspects, replacing “advocates” who often lack law degrees. For the first time in history, the presumption of innocence would be guaranteed in Mexico’s constitution.