Boobs on Bikes created a furore last year among residents who considered the topless parade indecent. They said it lowered the city's moral tone.
Protests, including several attempts by Christian groups to stop its progress, led to a heavy police presence as the procession wound its way along The Strand and Devonport Rd.
Yesterday's council meeting agreed unanimously to amend the bylaw in which the only circumstances requiring council permission to hold a parade were impeding pedestrian or vehicle access.
As well as making offensiveness one of the tests for requiring council permission, the meeting also added the potential for parades to cause a public nuisance or endanger public health.
The final wording would go out for public consultation.
Despite the backlash from some councillors against Boobs on Bikes last year, there was a complete absence of debate yesterday when the proposed bylaw change options were listed. There was a confidential legal opinion on the proposed changes.