Five of Virginia’s death row inmates alleged in a lawsuit Thursday that their nearly constant solitary confinement is unconstitutional and they should be give more freedom to exercise in the gym and see their immediate family members without a glass partition.

The lawsuit filed in federal district court in the Eastern District of Virginia asks that the five inmates be given the same privileges as inmate Alfredo Prieto, whose challenge to his own solitary confinement led a federal judge last year to rule that corrections officials could not impose such extreme isolation unilaterally and automatically. Prison officials have appealed that decision.

At stake in the lawsuit — as it seemed to be in Prieto’s case — is just how solitary life should be for Virginia’s death row inmates, and exactly what prison officials have to do in each case to justify imposing isolation. According to the Death Penalty Information Center, the state has eight inmates on death row, including Prieto and those involved in the more recent lawsuit.

The suit — filed on behalf of Thomas Porter, Anthony Juniper, Ivan Teleguz, Mark Lawlor and Ricky Gray — alleges that forcing death row inmates to spend nearly every hour of every day in small cells with “almost no contact with other human beings” is a form of cruel and unusual punishment.

All of those in the suit have been convicted of heinous crimes, including murders of a police officer and children.

The lawsuit says the inmates asked for the same privileges as those given to Prieto — who was allowed to exercise in the gym and see his immediate family without a glass partition after his legal challenge — but were denied. Prieto was convicted of murder in California and of killing a man and woman near Reston in 1988.

“It’s outrageous for the state to provide legally mandated relief for one of a bunch of similarly situated persons, particularly when what’s at issue is having to live in such horrific conditions,” said Victor M. Glasberg, one of the lawyers who filed the suit.

Although the lawsuit claims prison officials have relaxed the conditions under which Prieto was confined, Virginia officials have fought his case all the way to the U.S. Court of Appeals for the 4th Circuit, arguing that restrictive, solitary confinement conditions for death row inmates are necessary to keep the prison safe from people with little to lose.

U.S. District Judge Leonie M. Brinkema had rejected those arguments and ordered prison officials to either determine death row inmates’ confinement conditions on a case-by-case basis or to change all of their confinement conditions,“if only slightly,” so that they are not so restrictive.

The appeals court has not yet ruled on the case, and the ruling certainly could undercut the more recent lawsuit.

The five inmates — who have been on death row from three to nine years — do not suggest specific ways in which they should be given more liberties, except to say that they want to be treated like Prieto. They complain, though, that their cells are not adjacent to any others, and that they are only allowed to see family members for non-contact visits in a room with a glass partition. They also complain that the recreation room they are allowed to use for one hour a day, five days a week is a small outdoor cell without exercise equipment.

Michael Kelly, a spokesman for the Virginia attorney general’s office, said he could not comment because state lawyers had not yet reviewed the lawsuit.