The number of active Airbnb listings dropped by a third last month after Boston’s agreement with the big short-term rental company fully kicked in.

Airbnb had 5,500 listings when December started, a number that dropped to 3,780 over the course of the month, according to data provided to the city by Airbnb at the start of this month.

Airbnb in December began requiring city-issued registration numbers in order to post rental units. Airbnb — not the only short-term rental company operating in the city, but by far the largest — started that under an agreement with the city two months after a new Boston law went into effect in September that sharply restricted people offering short-term rentals and required them to register with the city.

A major goal of the new law was to cut down on the number of short-term rental units, returning them to the very tight housing market rather than constantly being used for short stays by visitors.

So far, 1,978 people have attempted to register with the city and more than 700 applications have been approved, but more — over 800 — have been rejected. The rest are still under review, per Boston’s Inspectional Services Department.

The number of units on Airbnb remains far higher than the number approved by the city, which the company said likely includes duplicate listings, long-term stays — the law doesn’t cover stays over 28 days — and illegal listings in the 30-day window before Airbnb takes them down.

“Going forward, we will continue to work with the City to take the appropriate action against listings, as needed,” Airbnb’s Kelley Gossett said in a statement.

ISD provided a breakdown of the registered units that showed that 73 properties have registered under the four exemptions outlined under the law: 63 existing lodging houses, seven furnished business stays, three bed-and-breakfasts and zero hospital-affiliated short-term stay spots.

Of the nonexempt properties, only three types of listings are allowed: People renting out their whole unit, people renting out a room in their unit, and people renting out adjacent units, which is only allowed in buildings with three units or fewer. Of the properties approved, 231 of the approved units are whole-unit rentals, 256 partial-unit rentals and 156 owner-adjacent rentals.

Last week, the city passed zoning changes to make it more difficult for people to make units into executive suites, a loophole the Herald reported on as a new trend in the fall.