City Council on Wednesday kicked off a review of the way the city handles accessory units on private property.

Only 18 of the units have been permitted since 2001, but three of those have been this year alone.

“You had an influx of them this year,” Planning Director David Hainley told City Council during Wednesday’s work session.

Accessory units — usually a separate, smaller living space on the same piece of property as a typical house — are allowed in any residential zone where the primary use is a single-family dwelling, Hainley said.

Often, residents request them for the use of an aging parent. But some not-so-neighborly disputes have spilled into council chambers during conditional use permit hearings in recent years, with neighbors accusing neighbors of renting the units to the general public, which is not allowed under city code.

“It appears that the process that we’re using now needs to be amended or at least reviewed,” City Councilman Mike Duman said Wednesday. He asked for the review after a recent hearing.

Suffolk regulates accessory units more than most neighboring localities in several respects, Hainley said. The rental restriction is not typical, for instance, and some other localities approve the units administratively, with no public hearing required.

Most on City Council wanted to move in that direction.

“I’m more in favor of loosening the restrictions,” Councilman Tim Johnson said. “I think when you own a property, an accessory dwelling is a right.”

Duman made a motion to restrict the zoning districts where the units are allowed to agricultural, rural residential and rural estate. But other council members pushed back.

“I believe we’re sort of attempting to over-regulate,” Mayor Linda T. Johnson said.

She noted that regulation of the rental business is futile with new websites like Airbnb allowing people to list bedrooms or accessory units for short-term rent.

“If people don’t do what they’re supposed to do once Airbnb takes off, it’s not even going to matter,” she said. “We’re not going to be able to do anything about it.”

Airbnb currently lists more than 300 available rentals in Suffolk.

Five council members voted against Duman’s proposal to further restrict the zoning districts where the units are allowed. But Tim Johnson then made a motion to study simply making approval of the units an administrative process, and everybody agreed with that.

A change to the city code will be brought forward at a future meeting.