HOUSTON -- Andrea Yates' capital murder convictions for drowning her children should be overturned because the state's expert witness falsely testified and Texas' insanity standard is unconstitutional, her attorneys argued Tuesday. A three-judge panel of the First Court of Appeals in Houston heard oral arguments Tuesday in Yates' appeal, which cites 19 errors from her 2002 trial. Yates' attorneys say she deserves a new trial. Jurors sentenced Yates to life in prison in the 2001 deaths of three of her children. She was not tried in the deaths of the other two.

Prosecutors say Yates' convictions should be upheld. They say there is no evidence their expert witness, Park Dietz, intentionally lied about consulting on an episode of the television series "Law and Order" that Dietz said dealt with a woman with postpartum depression being found not guilty by reason of insanity in the drowning of her children. He testified the episode aired in the weeks leading up to the drownings.

It was revealed after jurors found Yates guilty that no such program existed. Testimony during her trial indicated she watched the television series.

"That is the one thing in this case that allowed the state to say this wasn't psychosis, it wasn't mental illness -- it was a conscious plan. Without the testimony of Dr. Dietz, the state would not have been able to make their case," Yates' appeal attorney Troy McKinney said. "This case boiled down to a battle of the experts and the powerful testimony of Dr. Dietz ultimately prevailed."

Harris County Assistant District Attorney Alan Curry said Dietz's testimony about the television show came during cross-examination by Yates' defense attorney. There were three weeks of testimony that dealt with Yates' plans to kill her children, ranging in age from six months to 7 years, and her knowledge that doing so was wrong, he said.

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Attorneys: Yates Deserves New Trial Due To Flawed Testimony

"Dr. Dietz did not suggest by that testimony or elsewhere that (Yates) used that episode in order to assist her in planning, premeditating or calculating the killing of her children," Curry wrote. "There was a great deal of other evidence which revealed that (Yates) planned and/or premeditated her killing of her children."

Curry cited a tape-recorded police interview with Yates in which she said she had thought about killing her children for two years and in the weeks leading up to the drownings had filled the bathtub with water but "didn't do it that time."

Yates' attorneys claim the Texas insanity standard, which required the defendant prove she suffered from a severe mental disease or defect and did not know her actions were wrong, is unconstitutional because it does not define the words "know" and "wrong."

"(Yates) should not have been held responsible for her actions," her attorney George Parnham wrote. "While (Yates) may have 'known' that her actions would be considered wrong by others, her mental disturbance was so severe that she truly felt that she was doing the right thing."

Psychiatrists testified that Yates suffered from schizophrenia and postpartum depression, but defense and prosecution expert witnesses disagreed over whether it prevented her from knowing that drowning her children was wrong.

Jurors determined Yates knew it was wrong to kill her children and found her guilty.

Among the other errors cited by Yates' attorneys are the court's decision to show jurors the clothing the children were wearing when they died; the requirement that jurors be "death qualified" because the case involved capital murder charges, which can carry the death penalty; and the judge not informing jurors of the consequences of an innocent by reason of insanity verdict.

Yates, who will be eligible for parole in 2041, remains jailed at the Skyview Unit in Rusk, where she works in an outdoor flower garden and has janitorial duties.

Earlier this year, her husband, Russell, filed for divorce. He attended Tuesday's appeal and wasn't wearing a wedding ring.