Geography and gender will be key in selection of ministers
Geography is set to play a major role in Taoiseach Enda Kenny's appointment of junior ministers after nine of his senior posts went to TDs from Dublin and Cork.
Almost 20 Fine Gael TDs are understood to be in the running for positions but three of the 15 positions have already gone to Independents.
The Irish Independent understands three Ministers of State are set to be appointed to the Department of Health to help Simon Harris, including Finian McGrath, who has responsibility for disabilities.
At least one will also be assigned to the new Department of Regional Development and Rural Affairs, where Heather Humphreys is the senior minister.
Mr Kenny is expected to promote a number of female TDs, including Marcella Corcoran Kennedy and Helen McEntee - but backbenchers are privately warning he must not elevate first-time TDs "for gender reasons". Josepha Madigan has been tipped for a ministry despite being new to Leinster House.
Backbenchers say Mr Kenny must be extremely aware of the geographical split, with some "angry" that his Cabinet has nobody from west of Ireland, except Independent Denis Naughten.
The Taoiseach appointed seven ministers from Dublin, two from Cork and one each from Limerick, Laois, Wicklow and Monaghan.
"The whole area from Galway up to Donegal was ignored. It's not good enough," said one senior TD.
Four outgoing Ministers of State are still in the hunt for jobs and there is huge expectation on his backbenchers.
Dara Murphy (Cork), Michael Ring (Mayo), Joe McHugh (Donegal) and Damien English (Meath) will all be hopeful of retaining portfolios.
Sources say Mr Murphy and Mr McHugh may maintain their current positions as Minister for European Affairs and Minister for Gaeltacht Affairs respectively, as they only took office in 2014.
The Irish Independent understands Mr Ring is keen to remain in the Department of Sport where he has proven popular over the past five years.
"It's important to have a strong Fine Gael person in there now, given that Shane Ross is in the senior ministry," said a source.
Among other names seen as frontrunners for promotion are Eoghan Murphy (Dublin) and Sean Kyne (Galway) who were involved in government formation talks at various stages.
A number of rural Independents were particularly impressed with Mr Kyne's performance and he is a fluent Irish speaker, which may prove an advantage. Finance Minister Michael Noonan is thought to be backing Pat Breen from Clare for a move up the ranks, while Mr Kenny may also give a nod to John Deasy (Waterford) as a peace offering to the backbencher who has often been vocal in his criticism of the leadership.
David Stanton (Cork), Patrick O'Donovan (Limerick) and John Paul Phelan (Kilkenny) are all in the reckoning.
Kildare TD Martin Heydon is seen as having strong credentials for an agriculture post but ironically sources say his performance as an election poll topper bucking Fine Gael's national trend might go against him.
Meanwhile, Fianna Fáil leader Micheál Martin said he was "appalled" by two TDs tossing a coin over who should hold a junior ministerial post first.
Independents Kevin 'Boxer' Moran and Sean Canny will split a junior ministerial portfolio on a job share basis. "The idea that an hour before the Dáil is electing a Taoiseach and Government that there are people who are tossing up as to who will be minister for a year and who is going to become a minister for the following year is ludicrous," he said.