(CNN) -- A Texas court on Wednesday cleared the way for Andrea Yates to be tried a second time for drowning her children in a bathtub.The Texas Court of Criminal Appeals, the state's highest criminal court, left intact a lower court's decision that overturned Yates' convictions. Many factors must be considered before another trial begins, including whether Yates is mentally competent to stand trial, her attorney Wendell Odom told CNN. (Watch what Yates' attorney had to say -- 3:05)Harris County District Attorney Charles Rosenthal told CNN he is "disappointed" with the decision, which he said set a "frightening precedent." "We'll be moving toward a new trial," Rosenthal said. "If they want to plead guilty, which I am guessing they will, we will listen to what they have to say." Yates' attorney George Parnham praised the court's decision. "It's a good day," Parnham said. "The whole issue of mental health, specifically women's mental health, has been championed in this decision." Parnham said a new trial is a mixed blessing, because Yates will have to relive the horror of her children's deaths, but added, "She needs to be found not guilty by reason of insanity."Yates mounted an insanity defense at her trial on two counts of capital murder in the deaths of Noah, 7, John, 5, and Mary, 6 months. One of the counts covered the two eldest children. She was not tried for the drownings of Luke, 3, and Paul, 2.Parnham told CNN he would try to strike a plea agreement that would send Yates to a mental health facility rather than prison. "She has been told that she will be retried" and is not looking forward to returning to court, he said. "She would gladly forgo this process," Parnham added "but, you know, the right thing needs to be done here, and we're going to do it." In January, the lower appeals court found that an expert prosecution witness, Dr. Park Dietz, presented false testimony. Dietz told jurors Yates may have been influenced by a "Law & Order" epidsode, but the episode did not exist. Yates is being held in the psychiatric ward of Rusk Penitentiary in Rusk, Texas, about 200 miles north of Houston, Odom said. Yates' attorneys said they did not seek her release after the ruling because she is receiving medical treatment for severe postpartum depression.Yates was convicted of capital murder in March 2002 and sentenced to life in prison.She had a well-documented history of postpartum depression and her attorneys argued that she suffered from postpartum psychosis. Copyright 2005 CNN. All rights reserved.This material may not be published, broadcast, rewritten, or redistributed. Associated Press contributed to this report.