More than half the 1,300 inmates at the D.C. Jail have been tested for COVID-19, with 304 having been tested on a single day in late May as corrections officials have continued battling a simmering outbreak in the jail.

According to data from the D.C. Department of Corrections, 714 inmates were tested from mid-March through May 29, with the biggest batch of testing coming on May 22 as part of a jail-wide survey of the virus’s spread. More than 200 inmates at the jail’s two facilities — the Correctional Detention Facility and the Correctional Treatment Facility — have tested positive for COVID-19 since March, and as of June 1, some 469 inmates are currently under quarantine. One inmate passed away in April.

Advocates for inmates say they are cautiously optimistic that conditions could be improving at the jail, where officials came under sharp criticism in the early weeks of the pandemic for not working to more aggressively curb the virus’s spread — especially as evidence surfaced nationwide that jails and prisons were becoming hot spots for COVID-19.

“We do have questions about the reliability about the sample test. We don’t know what procedures they used, we don’t know if they’re using the unreliable Abbott machines, we don’t know how they selected the 300 inmates,” said Steven Marcus of the D.C. Public Defender Service. “But if the results are reliable, it’s good news for the men and women at the D.C. Jail.”

Advocates say that testing should ultimately be made universal for staff and inmates, much like in Maryland, where last month Gov. Larry Hogan ordered universal testing at state prisons and juvenile facilities.

Earlier this spring, both corrections staff and some inmates filed separate lawsuits against the city, alleging that not enough steps — from personal hygiene to personal protective equipment — had been taken to limit transmission of the novel coronavirus. In mid-April, a federal judge agreed with the inmates and assigned independent inspectors to review conditions. The judge also ordered the city to take a number of steps to address the COVID-19 outbreak.

Marcus says jail officials have made progress on some elements of the judge’s order, others are still missing. “The jail has made steps in direct response [to the lawsuit], but what we have heard is still that there are gross deficiencies in sanitation at the jail,” he said, adding that there are also concerns around wait times for medical care.

The federal judge is expected to hold another hearing on the lawsuit, where she could require the jail to continue taking steps to prevent transmission of the virus — or demand that officials do more.

D.C. officials say that since the pandemic started, they have decreased the jail’s population by roughly 500 inmates. But it’s unclear they can do much more on that front, as a majority of inmates in the jail are under some type of federal custody. Marcus says the U.S. Attorney for D.C. and U.S. Parole Commission have generally opposed the strategy of releasing inmates early in order to decrease their risk of contracting COVID-19.

Staff at the D.C. Jail have also been hit hard by COVID-19. Since March, 80 workers at the jail have tested positive for the virus, and one life has been lost.