DAVID Cameron was precisely 17 lines into his speech at the Scottish Conservative conference yesterday before he raised the issue which supposedly dared not speak its name at that get-together.

True, he didn't dwell on the extra powers the Tories might or might not choose to hand over to Holyrood in the event of a No vote next year. But he did say that Scots party leader Ruth Davidson was "not afraid to look at how devolution can be improved". It was another clear sign that the Prime Minister wants something at least in the Tory manifesto for the 2015 Westminster election.

The Conservatives face a bigger dilemma than the other pro-UK parties when it comes to extending devolution – but perhaps an even greater need to address it.

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The dilemma is explained in a new paper on devo max, which was delivered with the astute political timing one would expect of its authors, Professor John Curtice and Rachel Ormston, the day before the Tory faithful gathered in Stirling.

It reminds us that while most Scots do not support independence, a clear majority would like to see Holyrood, rather than Westminster, in charge of taxation and welfare. In the 2012 Scottish Social Attitudes Survey 64% said the Scottish parliament should provide benefits and 56% wanted MSPs to be responsible for levying all taxes. (Just 34% would transfer defence and foreign policy to Holyrood, incidentally, hence the talk of devo max which, in so as far as it has been ever properly defined, means full control of domestic affairs.)

The interesting– and somewhat daunting – part of the study from the Conservatives' point of view comes when it drills down into who actually supports devo max. The new analysis shows the over-65s, people in middle-class jobs and Scots who strongly identify themselves as British are significantly more sceptical about devolving taxation and welfare. You don't need to be sitting in the Abert Hall in Stirling this weekend to make the link between those demographics and the Scottish Conservative and Unionist Party.

The figures explain why the Tories are in such a pickle on the issue: grassroots members are instinctively suspicious about further devolution; party strategists see the need to appeal more widely.

It's worth quoting the bit of Mr Cameron's speech which followed his fleeting reference to Holyrood powers. The Conservatives, he said, must be "a party for the city as much as the country, for the young as much as the old, for the nurse in Glasgow as much as the farmer in the Borders". For the Prime Minister the question of more powers goes hand in hand with modernisation. And for Ms Davidson that presents a tricky problem.

She won the leadership 18 months ago by tailoring her pitch to the membership, famously drawing a "line in the sand" on more devolution, but now finds herself having to pursue a different agenda. It's no wonder Tories on both sides of the devolution debate are concerned about what might happen next. The line-in-the-sanders were alarmed when in March she U-turned and set up a commission, led by Lord Strathclyde, the former Tory leader in the Lords, to develop policies to extend devolution. The more-powers group, most prominently Murdo Fraser, the defeated leadership candidate, is worried the initiative will come to nothing, or next to nothing.

Tory spin doctors managed to keep a straight face when they tried to persuade me that all this amounted to a "good starting point" for the commission (which, for the record, hasn't actually started yet. A couple of business figures are still being sought to join the panel, I was told).

Ms Davidson has promised to bring forward her devolution proposals before the independence referendum in September next year but the Tories remain the hardest of the pro-UK parties to read on the issue. We know the Liberal Democrats favour a federal UK giving Scotland something like devo max, and we know Labour are looking at devolving a package of taxes, including income tax, but want to leave welfare reserved to Westminster. But who knows where the Conservatives are heading? Judging by the way she sidestepped the question in a "rally for Union" speech yesterday, not even Ms Davison herself.