It is thought Mr Major will propose a declaration by heads of state at the Edinburgh summit. This would allow Denmark exemption from some of the parts of the Maastricht treaty to which opposition parties have objected - defence, common citizenship, monetary union and immigration policy.
A declaration would not have the binding legal status demanded by the Danish anti-Maastricht camp. But it might persuade voters that safeguards were in place. It could be justified by pointing to the new, more important role that summits of heads of state will have under the Maastricht treaty, which gives them the power to define 'political guidelines' for the EC.
In this way it might be possible to put the treaty to a new referendum in Denmark next year. Mr Major is on a tour of EC capitals before the Edinburgh summit. The planned statement underlines that his effort is partly to 'sell' a version of the summit to his European partners. This is founded primarily on a vision of change: persuading disenchanted voters around the EC, especially in Denmark and Britain, that life has really moved on since last year's Maastricht summit.
He will try to promote the idea that a new set of values - openness, subsidiarity, value for money - dominate EC institutions. But Mr Major's mission is also partly to warn other governments of the risks if it all goes wrong. Failure could dent economic confidence even further. And if there is no deal at all at Edinburgh, then the EC is facing a desperate situation. The Danish presidency, which follows, is likely to be taken up with preparations to seek a new referendum on Maastricht.
In exchange, Mr Major has things to offer. Despite the apparently hardline British approach to the budget last week, ministers have been dropping hints of possible concessions. There is the prospect of a European economic growth package of some sort, though the final shape is unlikely to become clear until the day of the summit. There may also be cash on offer to those countries grinding their teeth over the impact of a trade deal with the United States. The budget itself can be manipulated to squeeze a few million ecus. The rate of increase of EC spending could be increased slightly from the British plan.
Second, the British plan aims to cap spending at 1.25 per cent in 1999. This is also flexible, Britain has indicated. The difference could be enough to buy off the southern countries, demanding more for a planned Cohesion Fund. Last night Mr Major was due in Madrid, with Spain leading the charge for more cohesion cash. There will be rumblings from the more parsimonious countries if this fiscal lassitude goes too far. But Britain has already bought enough credibility from the northern states with its pledge of tight control on spending to bring them onside for any deal.
The third area of possible compromise in the British approach is over the abatement which guarantees a British rebate on contributions to the Community. By agreeing to freeze the amount of the refund, or amending the complex technical formula for constructing it, he may appease some of Britain's critics.
But the unanswered question is whether more will be demanded - concessions from Mr Major on speedy ratification of the treaty, for instance, or a tougher approach to the Danes.