One of the easiest ways to end up on Texas’ death row is to kill a cop.

Stickup artist Robert Jennings did just that, brazenly gunning down police Officer Elston Howard during the 1988 robbery of a Houston pornography shop. In his almost three decades on death row, Jennings slid through multiple appeals, glumly moving closer to an ignoble end in the Huntsville death house.

Then on Sept. 2, 12 days before Jennings’ scheduled lethal injection, judges at the Texas Court of Criminal Appeals stopped the execution with a 5-4 vote. The stay marked the sixth consecutive time since May that the judges halted an execution.

While the court offered no immediate explanation for its decision, Texas lawyers active in capital appeals have hailed the vote as evidence that the top criminal court has grown more sensitive to possible death penalty flaws. If true, they argue, the court would be in step with a national pulling away from capital punishment — a movement that could lead to the penalty’s abolition.

The Jennings decision came as top state and national judges increasingly have spoken out against the death penalty and the number of executions and new death sentences in Texas — the nation’s leading capital punishment state — has plummeted.

“What connects these recent stays of execution,” said Jim Marcus, co-director of the University of Texas’ Capital Punishment Center, “are serious flaws that undermine the integrity of the prior proceedings, including junk science, inadequate counsel and unconstitutional jury instructions. These problems are not new. What appears to have changed is that a more careful scrutiny of Texas’ defective death penalty process has resulted in greater intolerance.”

A Houston death penalty advocate, however, countered that death penalty foes and appellate lawyers have misread the significance of the stays, the tenor of popular opinion and the reason behind declines in death sentences and executions.

“Stays of execution are the rule, not the exception,” said Dudley Sharp. “Most cases have a series of stays prior to execution or reversal. Six cases in a row may be a mathematical anomaly, not a trend.”

Sharp said the number of death sentences has declined because fewer capital murders have been committed since the 1990s. He also attributed the decline in executions to the limited availability of drugs needed to carry out punishment.

“The drop in executions is due to the legal and supply problems of the lethal injection drugs, which is easily overcome by a change in execution method or state prison systems having their own internal compounding pharmacies.”

The first five Texas stays were granted to permit the condemned to pursue DNA testing, develop claims related to decadeslong stays on death row and establish that counsel improperly failed to investigate and present mitigating evidence.

Since Texas introduced lethal injection in 1982, 537 killers have been put to death. The annual total, though, has declined sharply from a high of 40 in 2000 to six this year. If three remaining planned executions take place — and no new cases are added — the 2016 execution tally will be the lowest since 1996.

Nationally, reports the Associated Press, 2016 executions may fall to a 25-year low.

With the Texas Legislature’s addition in 2005 of the life without parole option in capital cases, the number of new death sentences also dropped. Last year, Texas juries assessed three death sentences; so far this year, only two.

While Gallop pollsters report that 61 percent of Americans support the death penalty, a Public Religion Research Institute survey found less than half favored executions when life without parole was an option.

Former Gov. Mark White, who oversaw 19 executions in his 1983-87 term, suggested that a growing recognition of problems in the state’s capital punishment procedures has led to the “death penalty being used less and less.”

While he philosophically supports the death penalty for the worst of the worst, he conceded that some innocent people may have been executed in Texas and cited a “desperate need to correct” the system’s failings.

“There are multiple pitfalls,” he said, “from commission of the crime to collecting evidence to apprehension of the suspect to the manner in which they are interrogated to the way a prosecutor selects a jury.”

Judge Elsa Alcala, a Gov. Rick Perry appointee to the Court of Criminal Appeals, also has highlighted what she perceives as “serious deficiencies” in the Texas capital protocol.

“We see cases over and over again where 10, 20 years later you find problems,” she wrote in a June opinion in the case of Julius Murphy, a Bowie County man convicted of robbery-murder.

Alcala stopped short of calling for capital punishment’s abolition, but in July, U.S. Supreme Court Justice Ruth Bader Ginsburg observed that the ultimate punishment is “fading away.”

“Most states don’t have any executions,” she told the Associated Press. “The executions we have are very heavily concentrated in a few states and even a few counties within those states.”

Last year, Ginsburg joined Justice Stephen Breyer in opining that the death penalty probably is unconstitutional.

allan.turner@chron.com