Many immigrants would have an easier path to challenging court decisions in deportation cases under legislation a top Senate Democrat plans to introduce Thursday.

The measure from Sen. Chris Murphy (D-Conn.) would update the legal standard for noncitizens claiming they had ineffective lawyers — bringing the process in line with other US court proceedings. Bloomberg Government first reported on the bill.

The proposal’s narrow scope reflects an effort by Murphy, who led doomed bipartisan border policy negotiations earlier this year, to build a foundation of small, pragmatic immigration measures that may draw support from both parties in the next Congress. Broader attempts to overhaul the US immigration system have been mired in politics for decades and face even worse odds ahead of the November election.

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“There are many ways our current immigration system is broken, and this legislation would provide one narrowly tailored fix to improve fairness,” Murphy said in a statement to Bloomberg Government.

The legislation focuses on a legal precedent known as Matter of Lozada. The 1988 Board of Immigration Appeals case set out a process for immigrants to reopen their deportation cases based on ineffective counsel. They must file an affidavit, inform the lawyer in question, and file a bar complaint against them, or explain why they haven’t.

The steps, particularly the bar complaint, are more onerous than those required in non-immigration court cases. Murphy’s bill would instead apply the same legal precedent across the board, relying on the standard the Supreme Court set in a 1984 case that applies to ineffective counsel claims in non-immigration cases.

“Claims of ineffective assistance of counsel for immigration matters should be handled the same way as every other legal proceeding,” Murphy said. “It’s a simple bill to bring consistency to our legal system and eliminate bureaucratic red tape.”

Immigration lawyers have long pushed for the change, saying the bar complaint requirement discourages lawyers from taking immigration cases and creates unfair red tape for immigrants pursuing their right to appeal.

“It works as a barrier,” Rekha Sharma-Crawford, a Kansas City, Mo.-based immigration attorney and treasurer of the American Immigration Lawyers Association, said in an interview. “Is somebody going to retaliate against me? Is the system going to retaliate against me? Those are real fears.”

The immigration lawyers group supports Murphy’s bill.