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UPDATE (March 2, 2015 3:25 PM): Judge Webb Baird denies Eric Wiiliams’ hopes for a new trial, sends him back to Death Row. More Details Here.

KAUFMAN (CBSDFW.COM) – Attorneys for Eric Williams are back in court on Thursday, arguing that their client deserves a brand new trial. Williams was convicted of killing former Kaufman County district attorney Mike McLelland and his wife, Cynthia McLelland, along with prosecutor Mark Hasse.

Hasse was killed two years ago just outside of the Kaufman County courthouse. The incident rattled those who work at the building, and throughout all of Kaufman County. Williams returned to the courthouse for a hearing on Wednesday, but waived his right to be there again on Thursday.

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Attorneys for Williams argue that the conviction and death sentence should be overturned.

First, attorneys stated that there is new evidence showing that Williams had a prior brain injury. That injury could have affected Williams and his ability to make sound decisions.

In an initial hearing held on Wednesday, a neuroradiologist testified that the convicted killer’s brain had been severely damaged and was abnormal. Head injury or diabetes could have caused the brain damage, and that may have even led to violent outbursts.

“All of the areas of the brain we’ve been discussing are connected,” the doctor testified. “When you have abnormalities in that part of the brain, that part of the brain is going to have a difficult time functioning normally.”

This information was not brought up during the original trial because it did not surface until afterwards.

Second, it has been suggested that the judge in the original trial made facial expressions at defense attorneys during the proceedings. Those actions, attorneys said, may have influenced the jury.

Williams was convicted back in December.