Hearts have appealed to supporters to buy Scottish Cup semi-final tickets or risk not getting equal allocations again.
The club were handed what they said was an equal initial 21,000 allocation for their April 21 game against Rangers at Hampden.
Chief executive Andrew McKinlay said in a club video: “We have got about 4,000 left to sell and, as has been well-documented, we fought hard to get half the ground.
“Why did we do that? One, because we think it is important and fair, but also because it will be massive for the team to come out and look round and see half that ground full of maroon. Therefore it’s really important for us to fill that.
“And also, I think it’s really important that those who have already put their hands in their pocket, to thank them for doing that, because there are already over 16,000 who have already done that and that’s not to be sniffed at.”
Hearts agreed to underwrite the cost of any unsold tickets as part of the agreement with the Scottish Football Association.
With adult tickets costing £30 or £40, the club are facing a six-figure cost if they struggle to sell more.
“Yes, there will be a cost to us if we don’t do that, that’s been talked about, but more importantly for me, if we don’t do it, in the future we may struggle to get half the stadium,” McKinlay said.
“I think it’s really important that we do that so we can get half the stadium.
“I know people are struggling financially at the moment, I know there’s a lot of calls on money and so I would just ask, if people are able to come, or bring people with them, they do so, so we can absolutely sell out our end.”
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