HOUSTON — A law firm that’s been representing Texas death row inmates for more than two decades is recommending the state establish a system for condemned prisoners to have better legal help during the initial appeal that follows their trial.

The Texas Defender Service this week released a report that examines what’s known as direct appeals in death penalty cases. It cited “systemic weaknesses” in the way those appeals are handled, contending lawyers are overwhelmed by caseloads and underpaid for the time they spend on these cases, that some attorneys who do accept the cases are inadequately prepared and that no entity in the state is devoted to training or consulting with lawyers handling direct appeals.

“The direct appeal framework for Texas death penalty cases is fraught with structural weaknesses,” the legal group concluded in its report, adding that those weaknesses heighten the likelihood that convictions and death sentences will be upheld when the appeals are reviewed by the Texas Court of Criminal Appeals, the state’s highest criminal court.

In direct appeals, attorneys review the trial court record for potential errors.

The legal firm is calling on the Legislature to consider establishing a statewide capital appellate defender office to represent death row convicts in their direct appeals, a statewide appointment system with caseload controls and uniform pay rates, and appointment of two lawyers — rather than one now required — to handle direct appeals.

“Deficient representation squanders scarce criminal justice resources, undermines the integrity of the Texas criminal justice system and warrants immediate attention from stakeholders,” the 56-page report said.

The group’s recommendations are based on a review of documents from the 84 direct appeals to the Court of Criminal Appeals during the seven-year period ending Dec. 31, 2015.

In its study, the Defender Service said it found the direct appeal attorneys had inadequate resources, excessive caseloads, inadequate briefing and showed “routine avoidance” to filing reply briefs and applying for review by the U.S. Supreme Court.

Capital murder defendants in need of legal help — most of whom are indigent — already have a regional public defender for trials in most rural areas of the state. State lawmakers in 2009 created the Office of Capital Writs to handle later appeals. The Defender Service is recommending such formal legal availabilities be extended to the direct appeals process, where it argues the quality of representation has remained “unexamined.”

Roe Wilson, who heads the Harris County District Attorney’s Legal Services Bureau, which handles capital case writs in the county that has sent the most inmates to death row, questioned the need for two defense attorneys to handle a direct appeal.

“In a direct appeal, you’re limited to the record itself, there’s no outside investigation,” Wilson said Wednesday. “It literally comes down to reading the record, identifying claims, doing the legal research and writing. I don’t know why it would take two people to do that.”

The report, however, pointed out that county prosecutors have more ready access to resources, such as auxiliary staff. Of the 84 cases in the study, two-thirds were handled by solo practicing attorneys. None of the 84 convictions was overturned by the Court of Criminal Appeals. The death sentence was overturned in three of them.

Wilson said defendants have better chances later in the appeals writ process because factual claims outside the trial record can be presented and investigated.

“It’s very difficult to get any case, not just a capital case, overturned on direct appeal because you are limited to exactly what’s in front of you,” she said.