Of all the execution methods being considered in the Mississippi senate last week, it was the firing squad that was rejected; nitrogen hypoxia and electrocution are still being considered. 

Discounting the firing squad is understandable, as Radley Balko explains:
“We recoil at methods such as the guillotine, hanging and the firing squad as barbaric anachronisms of a different era, when crowds gathered to witness and revel in the event.”

Bryan Stevenson highlights a similar disquiet at having to protect marksmen:
“The firing squad – they go out of their way that not all the guns have real bullets, so that the marksmen can walk away thinking, I didn’t do it. But there’s still this dead body on the ground. If we feel the need to actually protect the moral misgivings of the people participating, then there is no greater evidence of what we are doing is wrong.”

From the point of view of the person being executed, however, the firing squad appears to be a less cruel option than the alternatives, as US Supreme Court Justice Sotomayor pointed out last month in a significant dissent to a petition from Alabama:
“[T]he available evidence suggests that a competently performed shooting may cause nearly instant death. In addition to being near instant, death by shooting may also be comparatively painless. And historically, the firing squad has yielded significantly fewer botched executions.”* 

She adds that, in contrast,
‘Science and experience are now revealing that, at least with respect to midazolam-centered protocols, prisoners executed by lethal injection are suffering horrifying deaths beneath a “medically sterile aura of peace.”’**

It seems, then, that Mississippi’s greatest concern is not to avert “cruel and unusual punishment”, but to prevent public opposition to executions. To paraphrase Bryan Stevenson,
“If we feel the need to actually protect the moral misgivings of the public, then there is no greater evidence of what we are doing is wrong.”

*Thomas D. Arthur v. Jefferson S Dunn, Commissioner, Alabama Department of Corrections, et al, On Petition for Writ of Certiori to the United States Court of Appeals for the Eleventh Circuit, decided February 21, 2017, Sotomayor, J., dissenting (page 41 of the Supreme Court of the United States’ Order List 580 U.S., Tuesday, February 21, 2017) 

** Thomas D. Arthur v. Jefferson S Dunn, Commissioner, Alabama Department of Corrections, et al, On Petition for Writ of Certiori to the United States Court of Appeals for the Eleventh Circuit, decided February 21, 2017, Sotomayor, J., dissenting (page 39 of the Supreme Court of the United States’ Order List 580 U.S., Tuesday, February 21, 2017)