After the first public hearing under a revamped application process for exempting nonprofit organizations in the city from taxes, City Council members voted Wednesday night to give the Obici Healthcare Foundation a break.

The foundation would have owed about $17,324 on its new $1.79 million headquarters at the corner of North Main Street and Finney Avenue.

The new process, approved in September, requires organizations to make application for exemption and then have a public hearing at a City Council meeting. The new process came about as a result of the city assessor finding that many organizations in Suffolk had not obtained exemption approval through the proper avenue, putting them technically out of compliance, through no fault of their own, with city procedures.

“We certainly hope you will approve it,” said George Birdsong, chairman of the foundation’s Board of Directors, during the public hearing. “We’re a bona fide charitable organization. We do happen to be a large one, and that’s a good thing.”

The foundation has assets of $90 to $100 million, Birdsong said. It gives away roughly 5 percent each year to local organizations that support health-related initiatives in the area.

“We are strictly health-related,” Birdsong said. “That’s what all these funds are going to each year.”

One of the 10 criteria for organizations applying for the relief stipulates that the organization must provide at least 50 percent of its services to Suffolk citizens.

The foundation provided only 45 percent of its services to Suffolk citizens in the last fiscal year, but that figure was 73 percent the year before.

Councilman Robert Barclay said he thought it was important to look at a broad range when considering such things, and noted that the five-year average for the organization is well above 50 percent.

“If they meet all our criteria, there’s no reason we can’t approve the request,” Barclay said.

All his colleagues agreed — the motion passed unanimously.