For eight years Fulton County officials have labored under the watchful eye of a federal judge to address overcrowding and other problems at their troubled Rice Street jail.

Now, as they prepare for another court hearing next week, Fulton officials have taken steps they hope will eventually put an end to litigation that has led to hundreds of millions of dollars in expenses.

Last week the Fulton Board of Commissioners approved a 2014 budget that includes $2.1 million to send hundreds of inmates to other jails. That should get inmates who have been sleeping on the floor into better accommodations.

They also added $3.5 million to their budget to address staffing shortages at the jail and other county departments.

Commission Chairman John Eaves hopes those steps will help persuade U.S. District Judge Thomas W. Thrash to release the jail from his supervision by the end of the year.

“It’s been a lot of heavy lifting to get to where we are,” Eaves said. “We’ve made it a priority. We’ve made real progress.”

But it’s far from certain the judge will agree. The Southern Center for Human Rights has asked him to determine whether the county and Sheriff Ted Jackson are in contempt because of lingering problems. As recently as this week, about 160 inmates were still sleeping in temporary bunks on the jail floor.

Melanie Velez, an attorney for the human rights group, said getting them off the floor would improve conditions for inmates and employees alike. But she wanted more information about the county’s recent actions before conceding all is well at the jail.

“We have been urging this necessary step for many months and welcome the news that the county has allocated the money for doing so,” Velez said.

Thrash’s decision on the center’s contempt motion will be another turning point in a lawsuit that has bedeviled Fulton for a decade.

The center filed the lawsuit in 2004, citing crowded, dirty and dangerous conditions at the jail. Eighteen months later the parties agreed to a consent order that called for major renovations, minimum staffing requirements and a cap of 2,500 inmates at the jail, among other measures.

Fulton’s efforts to comply with that order have cost taxpayers more than $200 million for renovations, outsourcing inmates and other costs. The county is currently spending $4.8 million to replace 1,400 faulty locks that inmates were able to pry open. The work will be finished in May.

But replacing the locks has displaced inmates, and many have been sleeping on the floor. To address the problem, commissioners recently approved agreements with Cobb, DeKalb, Douglas and Gwinnett counties to house up to 265 displaced inmates until the work is finished.

Eaves said all inmates should be off the floor by Thursday’s hearing.

Commissioners approved $2.1 million to send inmates to other jails in the 2014 budget they approved this week. It will pay to send the prisoners to other counties, but also to lease the Union City jail — where Fulton can house up to 285 female inmates — through the end of the year.

Commissioners also approved $3.5 million to pay off accrued vacation time when employees leave. Currently, if an outgoing employee has two months of accrued vacation, Fulton can’t replace that employee until his vacation time is paid off in two months. That’s caused significant staffing shortages at the jail, Eaves said.

The extra money will allow Fulton to pay off vacation balances and replace deputies more quickly.

Eaves said those measures give the county “wiggle room” to find a long-term solution to jail overcrowding. The most obvious solution: buying the city of Atlanta’s jail.

The city and county have long discussed a possible sale, but in 2011 commissioners rejected a deal when Atlanta raised its asking price from $40 million to $85 million. Eaves said no formal talks are under way, though he said each side has expressed a willingness to revisit the issue.

“There’s a dance going on between two dance partners who don’t want to touch each other,” Eaves said.

Despite recent progress, Fulton has a history of backsliding on its jail commitments. Since 1982 the county has been sued three other times over jail conditions and the care of inmates. Each time it was released from court supervision, jail conditions deteriorated.

Fulton also has dragged its feet during the current litigation. In 2011 U.S. District Judge Marvin Shoob — who oversaw the jail until recently — threatened to throw county commissioners in federal prison if they didn’t address significant overcrowding. And commissioners postponed a vote on replacing the jail locks for months before finally consenting.

In October, the Southern Center for Human Rights asked the court to hold the county and the sheriff in contempt for continuing violations of the consent order. Hundreds of inmates were sleeping on the floor, and some roamed freely in the jail because the locks still weren’t fixed.

Commissioners and the sheriff blamed each other for the problems, and Thrash called for next week’s hearing to sort it out.

A year ago Shoob rejected the county’s request to terminate his supervision of the jail. Next week county officials just want to avoid a contempt citation. But Eaves plans to try again to end federal supervision later this year.

“We’re making a good-faith effort to satisfy everything,” he said.