Critics say the alarm infringes young people's rights
The decision on whether to ban so-called "mosquito" devices on council buildings has been delayed by a city authority.
The alarm emits high-pitched sound waves which are normally only audible to those under the age of 25.
They are designed to drive young people away from places where vandalism and bad behaviour are a problem.
After debating the issue, the leader of Plymouth City Council said she did not want a "knee jerk" reaction.
In August the city council installed 22 devices at a site in Whitleigh where vandalism had caused £54,000 of damage over a 12-month period.
Since their installation, the problem of vandalism has improved, but critics of the alarms believe they are indiscriminate and infringe on young people's human rights.
A council scrutiny panel had recommended a ban on the use of mosquito alarms, but councillors have now asked for a more detailed report and the matter will be considered again on 16 December.
Council Leader Vivien Pengelly said it was a difficult decision which many local authorities would have to face up to in the future.
"We need to balance the needs of the whole community in an attempt to provide safety, security and respect," she said.
"I do not intend that we provide a 'knee jerk' reaction to this situation."