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As soaring crime overwhelmed New York City’s courts in the 1970s, state lawmakers came up with a fix to speed things up. The State Legislature decided that people facing less than six months in jail would have their cases decided by a single judge rather than a jury.

That law has had the unintended effect of depriving immigrants in the city of jury trials for crimes like prostitution and harassment, even though they face the stiff punishment of deportation if convicted, advocates for immigrants said.

This week New York State’s highest court carved out an exception to the law, declaring in a 5-2 decision that noncitizens are entitled to jury trials for deportable offenses under the Sixth Amendment, which guarantees the right to a trial by an impartial jury.

Immigrant advocates and civil rights lawyers hailed the ruling as giving all immigrants, not just those charged with serious crimes, an avenue under the Constitution to fight charges that could lead to their removal from the country and permanent separation from their families. But critics said it gave them more rights than citizens have and might lead to bigger backlogs in the criminal courts.