Lawyers for former Gov. Rick Perry are urging the Texas Court of Criminal Appeals to finish off the remaining charge in his indictment, ratcheting up their push to end the case against the presidential candidate.

The request comes a few weeks after a state appeals court dismissed one of the two counts in the case, delivering Perry's team its first major victory in the yearlong legal saga. The remaining charge accuses Perry of abusing his power when he threatened to veto state funding for a unit of the Travis County district attorney's office .

In a filing Tuesday, Perry's lawyers argued that the state's highest criminal court should toss out the rest of the indictment as a way of preventing the "judicial system from being complicit in undermining the very structure of Texas government." Perry's team sharply criticized how the Austin-based 3rd Court of Appeals arrived at its July decision letting the charge stand, accusing it of "drawing a wholly incorrect lesson" from previous cases and using an "erroneous framework" for assessing the charge.

The Office of the State Prosecuting Attorney also has its sights set on the ruling by the 3rd Court of Appeals. Lisa McMinn, who leads the office, said last week she was preparing to challenge the July decision, which struck down as unconstitutional a part of the Texas penal code that defines coercion.

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A Travis County grand jury handed up the indictment a year ago Saturday. It deals with Perry's threat to cut off funding for the public integrity unit unless Travis County District Attorney Rosemary Lehmberg resigned following a drunken driving arrest. At the time, Lehmberg's office housed the unit, which handles ethics complaints against statewide officials.