While NFL owners opted not to vote on a rule that would allow games to be flexed into a Thursday night kickoff, they agreed Tuesday to modify the existing rule and allow teams to play a maximum of two short-week games.

That means that while some teams could play two Thursday night games, others would not have any. Back-to-back Thursday night games, such as a Thanksgiving game followed by a Thursday night game the next week, would only count as one short-week game, so some teams could wind up playing three Thursday games.

“We’re interested in making sure that we get exposure for all of our clubs,” said Brian Rolapp, NFL executive vice president and chief media and business officer.

“We also believe that these national windows are for clubs that are playing well. We want to put the best teams in the best windows.”

While the tabled proposal and subsequent modification on the final day of the league’s annual meetings in Phoenix had support from a sizable number of clubs, others met it with tepid reactions, and some were adamantly opposed, including New York Giants owner John Mara, who called the idea “abusive.”

Mara said owner support for the proposal was close and said he’s concerned a vote will come up again at the spring league meetings in May and will pass. A flexed game would be announced 15 days before the scheduled Thursday kickoff.

“At some point, can we please give some consideration to the people who are coming to our games?” Mara said. “People make plans to go to these games weeks and months in advance. And 15 days ahead of time to say, ‘Sorry, folks, that game you were planning on taking your kids to Sunday at 1, now it’s on Thursday night?’ What are we thinking about?”

Mara also said he’s frustrated that the idea was presented to the owners at the league meetings this week with no advance warning.

“This should have been vetted with the health and safety committee, it should have been vetted with the competition committee, and it was not,” Mara said. “They just tried to push it through.”

NFL commissioner Roger Goodell pushed back against Mara’s assertion that the practice would be “abusive” to fans, saying the league is trying to balance the best interests of in-stadium fans with those watching on television from home.

“There isn’t anybody in any of our organization that doesn’t put our fans first,” Goodell said. “Providing the best matchups for our fans is what we do. That’s part of what our schedule has always focused on. Flex has been part of that. We are very judicious with it and careful with it. We look at all the impacts of that before a decision is made.”