Fraser Forster and Co. are zeroing in on a new goals lost best for Scotland's top division.
But, after conceding in the recent games against Partick Thistle and Ross County, they can afford to ship just one more in their remaining five matches if they are to beat the mark set by Martin O'Neill's team in 2001-02.
Though he bust a gut to help the Hoops set that defensive record, Johan Mjallby would happily see the back-line he is currently coaching replace his team in the record books.
The team from 12 years ago lost just 18 in their 38 games as they romped to the title.
In this season's 33 matches, Fraser Forster has picked the ball out of his net on 16 occasions.
It appears to be a tall order. But, given that, during this campaign, Forster kept clean sheets for 13 consecutive SPFL games, the precedent has been set.
This target, along with the team wanting to equal the points record of 103 - which they can do if they win every game - is what Mjallby believes will ensure they are ready to pick up where they left off, winning 2-0 at Tannadice, when they head to Fir Park on Saturday.
The Swede said: "We want to make sure we don't lose any more games.
"We want to blend in more youngsters, if we can, and also players who have not had the game time they had hoped for.
"But, we always want to win every time, so we have to pick the right team to do that.
"We have Kris Commons who wants to finish top of the pile when it comes to scoring goals.
"And we want to keep as many clean sheets as we can.
"We have the chance to break the record for goals conceded.
"That is still on the cards, even if it is going to be hard to beat.
"We have to find some incentives for the rest of the season because we can't accept they think they are on holiday already."
That's a message Neil Lennon and his backroom team will be hammering home to the players after their weekend off.
Mjallby warned of the consequences if this is ignored and said: "There's a lot to play for.
"We want good performances. And, if you don't perform, we have other hungry players waiting to step onto the pitch."
Mjallby is confident the high standards which have carried Celtic over the line in the title race with so many games to spare will be maintained.
And he is relishing discovering who picks up the individual awards when the votes for Player of the Year are cast.
He said: "I don't really like to point out a single player because I think it's been a team performance and effort this season.
"Virgil van Dijk has to be there, and also Kris Commons, with having scored so many goals.
"Scott Brown has had a terrific season as well.
"He's vital for us and has never played better for us.
"So, those three for me are probably stand outs. And you have Fraser, as well.
"I'd say those four are my favourites, and one of them should pick up the Player of the Year trophy."