An ordinance that would punish marijuana possession in New Orleans with a fine rather than jail time got some tweaks Thursday from the New Orleans City Council, which plans to vote on the amended proposal in two weeks.

The changes to the proposed law, which has been pushed by Councilwoman Susan Guidry, would still allow police to treat pot possession as essentially a minor citation punishable by a fine of between $40 and $100. By contrast, penalties under state law start with a fine of up to $300 and 15 days in jail and can range as high as eight years in prison.

Officers could choose whether to enforce the state law or the local ordinance.

Guidry proposed easing the possession penalties earlier this year. The major difference between her original proposal and the amendments introduced and approved unanimously Thursday is the elimination of warnings that would have been issued the first two times someone was caught with marijuana.

Guidry said she still supported the idea of issuing warnings before fines kick in, but that it proved to be impractical to come up with a system to track them.

Guidry’s proposal was sparked by changes in state law on marijuana possession last year that eased some penalties and removed minimum sentences that otherwise would have conflicted with her proposed ordinance.

It’s aimed at making sure the police and the local jail aren’t overburdened with enforcing penalties against what is increasingly seen as a minor offense.

The changes introduced Thursday are aimed at solving practical and legal problems with the system of verbal or written warnings in the original ordinance, Guidry said. Police do not have a system that would allow officers in the field to check on whether warnings already had been issued to an individual, and the warnings also could raise legal concerns because those who received them would not be able to challenge them, Guidry said.

Under the revised ordinance, the first time someone is convicted of possessing marijuana, they would be fined $40. A second offense would result in a $60 fine, and a third offense an $80 fine. Fourth and subsequent convictions would be punished with $100 fines. Police would be able to confiscate the drugs when they write the citations, Guidry said.

Those penalties would reset if someone goes two or more years without a conviction.

Because nothing the city does can override state law, police officers would be able to use either the city ordinance or the state law if they find someone in possession of marijuana.

Mayor Mitch Landrieu’s office and the New Orleans Police Department are “continuing to review the impacts” of Guidry’s proposal, Landrieu spokesman Hayne Rainey said. District Attorney Leon Cannizzaro’s office, however, has warned that the change would encourage illegal drug use and violence.

Councilman Jared Brossett said he had concerns that the proposal could allow officers to discriminate against minorities by slapping them with the stiffer state penalties.

Guidry said the city’s experience with its current pot possession ordinance, which allows officers to issue a summons rather than taking a suspect to jail, has shown that officers are not using that discretion in a discriminatory way.

The amended ordinance is expected to come up for a vote March 17.

Follow Jeff Adelson on Twitter, @jadelson.