The prisoners, Ralph Baze and Thomas Clyde Bowling, sued the state of Kentucky claiming that lethal injection amounted to cruel and unusual punishment.
A 2006 supreme court decision allowed the death row inmates to contest the constitutional validity of lethal injection used for execution across the US.
But the court had never agreed to consider the fundamental question of whether the mix of drugs used in Kentucky and elsewhere violated the Eighth Amendment's ban on cruel and unusual punishment.
In a judgment in September, however, the supreme court finally agreed to consider that question. The postponement of Berry's execution, and also of the other two, was consequential to that judgment.
The court is now expected to hear the Kentucky inmates' appeal before it goes into recess in July. Exploiting the 2006 court decision, several death row inmates had challenged lethal injection in lower courts on both constitutional and ethical grounds.
However, the lower courts reached conflicting conclusions on these petitions.
While the courts found that lethal injection as practised in California, Florida and Tennessee was unconstitutional, the practice in Missouri, Arizona and Oklahoma was constitutionally acceptable.
Meanwhile, taking a cue from the supreme court decision in September, several state and federal courts have put a moratorium on all scheduled executions until the high court's final verdict.
Executions have already dropped to the lowest level in over a decade. In 2007, they dropped to 42 from 53 in 2006.
The opponents of the death penalty in general and of lethal injection in particular expect that the court's decision on the Kentucky appeal will have a far-reaching impact on the future of the death penalty in the US.
If the court determines that lethal injection is cruel and unusual, the states will be forced to find a more humane way of execution.
History of lethal injection
The US began using lethal injection for execution in 1978 as an alternative to the traditional methods such as electrocution, gassing, hanging and shooting. That was one year after it re-introduced the death penalty ending a moratorium of five years.
| Opposition to lethal injection and the death|
penalty is gaining strength in the US [AP]
Today, a total of 37 of the 50 states in the country perform lethal injection as the mode of execution. They use the same three-drug cocktail that consists of an anaesthetic a muscle paralyser and a substance to stop the heart.
The opponents of injection argue that if the prisoner is not given enough anaesthetic, he will suffer excruciating pain without being able to cry out.
Eleven of the 37 states later discontinued the drug after opponents alleged that it was ineffective and cruel.
Opposition to lethal injection, alongside a demand to abolish the death penalty itself, is gaining strength across the US.
The American Bar Association (ABA) has renewed its call for a nationwide halt to executions following a series of state studies that found serious problems in their death penalty systems.
It has also called for the abolition of lethal injection which it said was deeply flawed.