Can the Irish public stomach paying more than half a million a year to the head of a bank we have pumped billions into?
Can they risk not paying more?
The issue lurched back into the spotlight this week following AIB chief executive David Duffy's shock resignation on Monday.
Just nine months after Duffy signed a three year contract, the lender's board and the Department of Finance must begin the search for his replacement.
Because of the cap on bankers pay that has been in place since 2011, the person they choose to lead AIB back into private hands can't earn more than €500,000 a year. That, it is becoming clear, is a big problem.
"Bankers making €500,000 a year are two and three levels down from CEO status," said Jeanne Branthover.
She is managing partner at international financial service recruiter Boyden New York and was named one of the world's top 50 most influential headhunters by Businessweek. She is paying close attention to the AIB search.
"If they are recruiting in the US it is going to be a huge factor."
The tasks facing Duffy's replacement include converting €1.6bn worth of convertible bonds and €3.5bn of preference shares owned by the State into equity and successfully bringing it through an IPO.
"Any client of mine in that situation would be asking for a seasoned chief executive that has experience of taking a firm through an IPO," she adds. "There has to be some kind of comfort involved for shareholders. And if you want a known chief executive, you are going to need to pay for that person."
It is "a constraint", Enda Kenny conceded from the margins of the World Economic Forum at Davos, Switzerland this week.
"You know, the wage caps are a constraint. And obviously, coming from where we've come from, that's been a difficulty".
But Mr Kenny is still very aware of how unpopular a decision to lift it would be.
"The Government will always act in the interest of the Irish taxpayer, he concluded. "The Government have absolutely no intention of changing the capping level."
The consequence, Ms Branthover and several other sources said, is that the eventual choice will come from inside the bank.Two have emerged as most likely, a well-informed senior banker said.
They are chief financial officer Mark Bourke, who before AIB was chief executive at financial services group IFG, and Bernard Byrne, its director of personal and business banking, formerly group finance director at ESB.
Yet history suggests that AIB rarely produces chief executives from within. It has a track record of appointing unexpected choices, often from overseas.
Nobody anticipated Duffy when he was announced in 2011. While he is Irish and was educated at Trinity College, he was headhunted for the job from Singapore, where he ran his own consultancy business, Celtic Advisory International. Most of his career was spent abroad. He started out at Goldman Sachs - the same firm advising AIB on its plans to go private - where for nearly a decade he worked on restructuring, followed by an eight-year stint at Dutch bank ING. His last job was as CEO of Standard Bank London.
Current chairman Richard Pym and predecessor David Hodgkinson also came from the UK. Hodgkinson moved from HSBC, where he was chief operations officer.
And not everyone is motivated by their pay cheque. Duffy regularly said he wasn't in it for the money, that fixing AIB was a principled job. The fact that he has now left for a much better paying role casts doubt on that, but the point still stands.
"There may well be someone with the right skills who just really wants to live in Ireland and deal with a state-owned bank" said Branthover.
One person who might just fit that bill is John Hourican - one of the most senior and experienced Irish bankers abroad.
Hourican was chief executive of markets and international banking for the RBS until 2013 when he left for Bank of Cyprus. He is in the midst of returning the nationalised bank to private ownership, attending investor roadshows all over the world - just like AIB's new top dog will have to.
But Hourican will be used to much higher pay than €500,000 - his salary alone at the Cypriot bank was €840,000 a year, never mind other benefits. And there are questions to be answered regarding his time at RBS. He quit the British bank in recognition of its LIBOR-fixing scandal.
There was no suggestion that he was involved - but that doesn't resolve the point that a business which he headed up was responsible for one of the most embarrassing and costly errors in the history of RBS.
The process is only beginning to begin. Executive search firms may be appointed. Duffy is contractually obliged to give six months notice and the bank has confirmed that he will definitely be kept around until March at the very least, when it issues its next set of results.
An appointment will be made "within months", Michael Noonan said on Wednesday, not within weeks. It took AIB more than a year to appoint Duffy, with former chairman David Hodgkinson filling in in the meantime.
Still, Europe's fourth biggest bank by market capitalisation does not have all day. Work to prepare for its return to private ownership has already begun, with the Government intent on getting some cash back before the next election.
So AIB's nominations committee will have to proceed, even if finding a capable candidate willing to work for a fraction of what their peers are seems impossible. The committee has undergone some membership changes in the past year, losing David Hodgkinson and former Tanaiste Dick Spring and gaining chairman Pym. The other four members are ex-NTMA chief and Goodbody stockbrokers chairman Michael Somers, former Intel VP Jim O'Hara and ex-Merrill Lyncher Peter Hagan.
Theirs is a difficult job, Branthover concluded. "What Duffy did with AIB... there are not a million people who can do that."
Sunday Indo Business