A bill was on Monday night's city council agenda that would limit parking to two hours on streets surrounding the Edmond Office Plaza.
The decision would have required postal workers nearby to pay $25 a month to park in a garage a block away from their building.
The council sent the proposal back to the traffic commission to investigate it further.
"We have 75 carriers, we have twenty clerks, they have to park somewhere and some of them are coming in at 11:00 at night, some of them are coming in at three in the morning," said Glenn Wheeler, a postal worker affected by the ordinance. "You don't want to have to park two blocks away to get to work."
Postal workers say the decision to postpone the vote gives the Post Master the chance to apply for more spots.
There is no timetable for when a decision will be made.