Although the city's Assessors Office turned down the request, it has granted temporary adjustments for fiscal 1987 and 1988.
It is unclear whether the downzoning exemption might strengthen the club's abatement request.
Under standing city rules, the Fly Club is located in a residentially zoned area. But the city considers final clubs to be commerical property and taxes them at the commercial rate, which is significantly higher than the residential one.
The City Council has not yet ruled on the downzoning proposal, developed in a petition submitted by the East Cambridge Neighborhood Association.
The Crimson has also received an exemption from the petition to allow building renovations that will begin in 1990.
Kirsten L. Parkinson contributed to the reporting of this story.