Moore and Luna appeared in a downtown LA courtroom to provide information about how their respective departments are handling the matter.
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"That's why we are in court today: We want to make sure there is a fair and equitable system, a system that's constitutional," Luna told ABC7 in a brief interview outside the courthouse.
Back in May, the judge granted a preliminary injunction in a class action lawsuit. Under the ruling, the Los Angeles police and L.A. County sheriff's departments cannot require cash bail for certain people in custody before their arraignment.
Typically, when someone is arrested, the charges are set by law enforcement and come with a specific bail amount. Those who can't afford it have to wait in jail. Attorneys say that's what happened to several of their clients who were held for felony vandalism.
LA Superior Court to reduce reliance on cash bail in non-violent cases
"Two of our plaintiffs were arrested for this offense. Neither one was ultimately charged. Both were released after five days of pre-arraignment jail based on money bail," said attorney Taylor Benninger.
Meanwhile, the court system is also changing the bail system so that almost all defendants accused of misdemeanors or nonviolent crimes could be released. At Monday's hearing, the sheriff and the police chief told the judge they have concerns.
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"I do believe that bail, as a construct of the state constitution, provides protections for an individual's rights," Moore said. "But also what is the most primary consideration is the issuance of bail -- when a person is arrested and charged with an offense -- is the protection of the public safety."
Said Luna: ""We're not saying that zero-bail is completely out. We're saying if you have a repeat offender, someone who is a habitual criminal, they have to be held accountable -- even for a stack of lower level crimes."
Several of the new zero-bail rules are scheduled to go into effect on Oct. 1.