Two councilmembers, Andrew Burks and Wanda Adams, submitted amendments calling for changes to the city's term limits.
Right now, the mayor, city controller and councilmembers can serve up to three two-year terms.
Burks says those two-year cycles put the city's elected officials in a bind.
"We run for one year, we work one year, we run for one year and we work for one year. We really can't get anything done. By the time you're in your second year you're campaigning again. And so this would make it a lot easier for continuity for us to really get some things done. And it improves upon the ability of the councilmembers and the mayor to do a better job."
Burks wants the ethics committee to consider changing the two-year term to a four-year term.
Mayor Annise Parker has long expressed her support of changing the city's term limits.
Parker served as a councilmember for six years and as city controller for six years. She's now in her second term as mayor.
Councilmember Helena Brown was one of two opposing votes to the proposal.
"The inconvenience of us having to run and campaign every two years is to our advantage and the advantage of the citizens of Houston. Four years is too long a time for change out if we're not doing our job right and representing our people and being responsive to their needs. So I stand in opposition to this, thank you."
A similar proposal was floated at city hall two years ago, but councilmembers at that time voted it down and kept the measure from appearing on the ballot. This year, a new crop of councilmembers could be more inclined to bring the issue to the voters.