The Government has been weighing up a number of considerations as it prepares to appoint a successor to Mr Justice Keane, who retires as Chief Justice on Tuesday.
First and foremost it will need to nominate - for appointment by the President - someone with sufficient experience and background to command respect among the judiciary and wider legal world.
It will also be considering the likely direction the new Supreme Court will take, in the light of continued challenges to the authority of the Government.
The Attorney General recently outlined the thinking of the Government in this regard, stressing that the first place people should go to vindicate their rights is not to the courts, but to their elected representatives.
The Government will hope the highest court in the land will agree. Inevitably political affiliation plays a role in senior judicial appointments.
The name most commonly mentioned is that of Mr Justice Murray, who was appointed to the Supreme Court in 1999.
He had previously been the Irish nominee on the European Court of Justice in Brussels.
Mr Justice Murray has a long association with Fianna Fáil, having contested the local elections for the party in Dún Laoghaire in the early 1970s as a young barrister. He was unsuccessful. He was called upon to become Attorney General by Mr Charles Haughey in 1982, following the shock resignation of Patrick Connolly.
That government fell later that year, but he was renominated in 1987 and again in 1989. He went straight from that position to the European Court of Justice in 1991, and was reappointed to that court in 1997. It is widely thought he has been interested in the job of Chief Justice for a long time, and his wide European experience, his five years on the Supreme Court, and his political connections, make him a very strong contender. However, there have been surprise decisions before, not least when Mr Justice Ronan Keane was appointed 4½ years ago. He had not been the front-runner at the time.
The present President of the High Court, Mr Justice Finnegan, has also been mentioned in connection with the chief justice's position. There was some surprise when he was appointed president by the present Government, as he was far from the most senior judge on the High Court at the time, but since his appointment he has impressed those in the system with his hard work and attention to detail. As President of the High Court he is the next most senior member of the judiciary.
Prior to the appointment of Mr Justice Keane, the name of Mrs Justice Denham was frequently mentioned as the likely first woman chief justice of Ireland. She had just presided over a number of reports on the reorganisation of the whole courts system, and was credited with outlining a template for the modernisation of the system.
Her diplomatic skills, in bringing a sometimes conservative judiciary along with her, were widely praised.
She has continued this reforming work with the recently published report on procedures in personal injuries cases.
However, her appointment would involve a departure from the usual practice of nominating people to such positions who are politically close to the Government of the day.
This would not be such a problem with Mr Justice Hardiman, who as a barrister was associated with the Progressive Democrats and is a close personal friend of the Minister for Justice. His qualities as a jurist are highly regarded, and he has brought a new sharpness and consistency to the Court of Criminal Appeal, over which he presided.
But would the Fianna Fáil majority in Cabinet be prepared to offer such a prize to someone associated with the junior partner in Government, especially in the light of the reported disquiet in party ranks over PD influence? It is not thought likely.
There could, however, be an impasse, and this could create the circumstances for a surprise.
Some observers have said that the prospect of the appointment of Mr Justice Geoghegan should not be ruled out. He has a long and distinguished history as a jurist, and would be a steady pair of hands.
Whoever gets the job will face unprecedented challenges, as the judiciary deals with the new procedures brought in to deal with the Curtin affair.