By Adrian Croft and Rodrigo De Miguel

MADRID (Reuters) - Prime Minister Mariano Rajoy is expected to turn to trusted allies on Thursday when he names a cabinet that will need to make tough budget decisions and juggle the demands of other parties if his minority government is to survive.

Rajoy has given no public hints about his team since he won support for a second term in a parliamentary confidence vote on Saturday, after two indecisive elections that led to 10 months of political paralysis.

He is widely tipped to retain Luis de Guindos as economy minister, with Spanish media suggesting he may give extra responsibility to a man generally respected by his counterparts abroad after steering Spain out of recession and into a strong recovery under Rajoy's first government.

Conservative People's Party (PP) leader Rajoy, 61, governed with an absolute majority between 2011 and 2015, a period when unemployment peaked at 27 percent and Spain's banks needed a 41 billion euro ($45 billion) European bailout.

Now heading a minority administration, Rajoy will also need particularly firm hands at the tiller for liaising with a fragmented parliament and with Spain's autonomous regions.

According to El Mundo newspaper, he will also retain Soraya Saenz de Santamaria, often the public face of the party in news conferences, as deputy prime minister, and promote PP stalwart and former Castilla-La Mancha regional government head Maria Dolores de Cospedal.

Following the June election in which the PP finished first, Rajoy will be able to count on backing from the liberal Ciudadanos (Citizens) party, the fourth-largest group in parliament, on 150 previously agreed measures to tackle political corruption and reform the electoral system.

Even with Ciudadanos' backing, Rajoy's PP lacks a majority. He has said he is ready to engage in the negotiations that approving new laws will require, but winning support from a skeptical Socialist party or smaller regional parties will not be easy.

TOO MANY COOKS?

The 2017 budget will be a priority for the new government.

Spain, the euro zone's fourth biggest economy, needs to shrink its budget deficit to 3.1 percent of output in 2017 from an expected 4.6 percent this year to meet targets agreed with Brussels.

It currently has two ministers handling economic matters, de Guindos and acting Treasury Minister Cristobal Montoro, and insiders say this has made it difficult for Madrid to speak with one voice to Brussels on budget matters.

Based on its latest budget plan, Spain would need 5 billion euros in extra revenue or spending cuts to reach the target. But Rajoy said last week that whether new spending cuts were needed depended on how tax revenues performed.

The Socialists have said they would oppose any attempt to impose more cuts, and the other of Spain's 'big four' parties - anti-austerity Podemos - opposes Rajoy and his legislative program.

A staunch defender of Spanish unity, Rajoy will also have to grapple with an independence campaign by the wealthy northeastern Catalonia region, which plans a referendum next year on breaking away from Spain.

Rajoy will announce his new cabinet after briefing King Felipe at 1700 GMT, government sources said. It will meet for the first time on Friday.

($1 = 0.9033 euros)

(Editing by Angus Berwick and John Stonestreet)