RALEIGH, N.C.  The release of the third death row inmate in six months in North Carolina last week is raising fresh questions about whether states are supplying capital-murder defendants with adequate counsel, even as an execution on Tuesday night in Georgia ended a seven-month national suspension.

In all three cases, North Carolina appeals courts found that evidence that would have favored the defendants was withheld from defense lawyers by prosecutors or investigators. In two of the cases, including that of Levon Jones, who was released on Friday after 14 years on death row, the courts said the defendants’ lawyers had failed to mount an adequate defense. Nationwide, Mr. Jones’s release was the sixth in a year.

John Holdridge, director of the A.C.L.U. Capital Punishment Project, which provided representation for Mr. Jones, said the successful appeals showed that the problem with the death penalty was not the method of execution  the issue ruled on by the Supreme Court last month  but instead “poor people getting lousy lawyers.”

“All these states are gearing up to start executing people again, and nobody seems to be concerned about these systemic problems,” Mr. Holdridge said.