The modern American death penalty is beset with endless complications and contradictions, and over the years no state has embodied the full range of these as consistently as Georgia.

Death sentences handed down by Georgia provided the basis for both the Supreme Court’s 1972 moratorium on capital punishment and its lifting of that moratorium four years later. In 1987, the court upheld another Georgia death sentence — of a black man convicted of murdering a white police officer — despite statistical evidence showing that the death penalty there was applied far more often when the victim was white rather than black.

Now Georgia is in the spotlight again, as it prepares to execute Warren Lee Hill Jr. Mr. Hill was serving a life sentence for killing his girlfriend when he was convicted of the murder of a fellow inmate in 1991. He is scheduled to be put to death by lethal injection on Jan. 27.

Mr. Hill was scheduled to die in 2012 and 2013, but both times his execution was stayed. In 2013, a state judge stopped it because of constitutional concerns over a new law making the source and composition of Georgia’s lethal-injection drugs a state secret. Mr. Hill has long claimed he is intellectually disabled, with an average I.Q. score of 70. Seven mental health experts have all agreed with him. Three of them, all hired by the state, originally testified that he was competent, but later recanted.