GAA president John Horan anticipates that the Leinster and Munster Hurling Championships will incorporate a break week next season.
In the first year of the new round-robin format, Offaly, Wexford, Tipperary and Waterford were all dealt the short straw of playing four weekends in a row, and only the Yellow Bellies have avoided elimination.
"It seems to have had an impact on some of those teams that have got caught like that," Horan told RTÉ Radio 1's Morning Ireland, following today's All-Ireland SFC qualifier draw.
"There is an opportunity for the Munster and Leinster councils to come together next year.
"Leinster started a week earlier than Munster and finished a week earlier. If they both started at the same time, there would be a possibility of each Championship having a break on separate weekends, a rest weekend.
"I think that would be to the benefit of all teams involved."
‘By the time we see Wexford in a month’s time, they are going to be that ball of energy again that we are used to seeing’ pic.twitter.com/pYVTxYiRzz— The Sunday Game (@TheSundayGame) June 10, 2018
Speaking earlier in the same programme, former Kilkenny star Eddie Brennan also supported such a move.
Tipperary and Wexford were both beaten at the weekend, despite holding half-time advantages against Clare and Kilkenny respectively.
"Three of the four teams that had to play four weeks in a row are gone out of the Championship, and Wexford have flatlined a bit towards the end of matches.
"Overall, it (the new structure) has been very positive but you would have to say that this time next year you’d be hoping and praying that you’re going to get a break in the middle, just to re-energise and get going again.
"Definitely, there’s a tweak needed so that everybody plays the same weekends and rests the same weekends, then it’s absolutely a level playing field."
Horan also ruled out any reconsideration of the promotion-relegation rules until the end of the trial of the new format in 2020.
Offaly will play in the Joe McDonagh Cup next season and will be replaced by Westmeath or Carlow, who meet in the second-tier final on 1 July.
"Personally, I think it’s unnecessary to make a tweak of that nature at this early stage," said Horan.
"We’ll let it take its course and see how it runs after another two years."