Michael Duignan has expressed disappointment that crowd sizes at GAA matches will not be increased beyond the current 200 person limit, outlining his view that it should be linked to the scale of the venues.
On Tuesday, the Government again delayed the country's entry into Phase 4, which means that sporting attendances will remain restricted at least for the coming weeks before the decision is revisited.
Speaking to Darren Frehill on RTÉ Radio 1's Morning Ireland, Offaly county board chairman Duignan felt larger venues should have seen an increase in the attendance limit.
"It's understandable that in some smaller venues 500 would be a big crowd and it would be hard to social distance," he said.
"But in Offaly, for example, O'Connor Park capacity is 20,000. Birr, again a county ground, we could easily hold that sort of crowd safely and maybe a lot more as well.
"It was that compromise that people were looking for. Across society, people are looking for capacities to be linked to the size of the venue. I don't think one size fits all is good enough at this stage."
The financial impact of crowd restrictions on county boards is an issue Duignan is remaining mindful of ahead of the return of inter-county action later this year.
"It takes a lot of money to run a county board and our main funding comes from our crowds," he said.
"Last year in Offaly, we would have done close to €400,000 on gate receipts. Galway would have done close to €1 million.
"Without that money, without that income, even allowing our teams to go back training, it won't happen because we don't have the money.
"Certainly, I can speak for Offaly. We are looking at a huge deficit for the year as it is and our only hope of getting back to parity was having decent crowds at our matches and that's not going to happen for the foreseeable future."