Blount, who is accused of fatally shooting Gary police officer Jeffrey Westerfield, and Darren Vann, accused of slaying seven women, are each facing the death penalty in cases before the Lake County Superior Court.
They each have argued in recent court filings that Indiana's death penalty law is unconstitutional.
On Thursday, their attorneys presented their arguments before a judge.
While the two defendants have separate, unrelated cases, their attorneys made many of the same arguments, even playing off what happened in the other's hearing. Lawyers on both sides got into the nitty gritty of their arguments, with Judge Samuel Cappas flipping through a reference book as the attorneys referenced stacks of court cases.