Right-wing methods should be used to achieve the aims long held by moderate Conservatives, leadership contender David Davis has said.
David Davis says he wants to help the poorest in society
In a speech on Wednesday, Mr Davis embraced a "new Tory idealism" and said he wanted those "at the bottom of the pile" to achieve their dreams.
Rival Ken Clarke says he and Mr Davis are in a two-horse leadership race.
But Liam Fox insists his newly-launched campaign is gaining momentum and he is setting out his vision in a speech.
Mr Davis is still the bookmakers' favourite to succeed Michael Howard.
He has yet to announce he will be a candidate in the leadership race and told BBC News: "When and if I declare will be when it suits me. It will be when the rules are determined."
Mr Davis said he was "not remotely worried" he was losing ground to his rivals.
He admitted that Ken Clarke had made a "very stylish" start to his campaign, but claimed he was not surprised or bothered by that.
Mr Davis outlined his plans to the Institute of Public Policy Research in London.
The shadow home secretary said Tories had been too timid in recent years about explaining how they wanted to improve society.
DAVIS' TORY PRIORITIES
Rebuilding a "low tax, low regulation, free enterprise economy"
Boost law and order forces, reduce the fear of crime and punish criminals effectively
Take decisions "as close as practicable to local communities"
Give people more choice in public services, break monopolies, reduce targets and encourage competition
Recognise the central role of the family in both the tax and welfare systems
Tackle welfare dependency
"We sometimes behave as if the Left, with their vocabulary and their policies, had acquired a freehold on social policy," he said.
"I stand for a new Tory idealism. I want to achieve the aims that moderate Conservatives have always championed; a strong society based on a free economy, with opportunity for all.
"To achieve those aims we need the methods which have been championed by thinkers of the right; decentralisation, less state intervention, competition and choice."
Measures of compassion
The Haltemprice and Howden MP set six priorities for the next Conservative government, including lower taxes.
Mr Davis said the party should help individuals and families achieve their ambitions but must not play the role of the family or community.
Helping those at the bottom of the pile is the right thing to do, not something driven by focus groups, he argued.
"I don't measure compassion by the amount of taxpayer's money spent; I measure it by the change we make to people's lives," added Mr Davis.
Dr Fox will also focus on social problems as he elaborates on his theme of a "broken society" in a speech in London.
He tells the Daily Telegraph newspaper: "If you look at what has happened under Blair 'the healer', we've got a rise in teenage pregnancy, a rise in the abortion rate, a rise in violent crime and a rise in domestic violence.
"If these things don't say to us our society is becoming dysfunctional, I don't know what does."
The shadow foreign secretary argues the Tories must make the moral and economic case for lower taxes.
And in a clear dig at Mr Clarke, he says it is difficult to believe people who have always been committed to a certain model of Europe have undergone a "Damascene conversion".
But in an interview for The Times, Mr Clarke says the leadership choice must not come down to European battles.
"If the only reason I am defeated is because of Europe as a defining issue, I fear the Conservative Party will be in opposition for a very long time to come," he says.
Among the other leadership hopefuls, Sir Malcolm Rifkind is meeting ex-steel workers in Cardiff who lost their pensions after their employer went into receivership.