Ireland's EU presidency has proposed the deletion of articles in the draft constitutional treaty that would abolish national vetoes in some areas of tax policy.
A new draft, which will be considered by EU foreign ministers in Luxembourg today, also proposes changes to articles concerning social security and co-operation on criminal matters.
If approved, the changes would meet the most serious objections raised by Britain to the draft treaty and improve the chances of an agreement on the constitution when EU leaders meet in Brussels later this week.
They also address some of Ireland's own political difficulties with the draft treaty drawn up by the Convention on the Future of Europe.
The new draft would allow EU ministers to introduce by qualified majority measures to improve judicial co-operation on criminal matters, including common rules of procedure. If any country feels that such a law "would infringe the fundamental principles of its legal system", however, it could demand that the issue should be referred to EU leaders, to be decided unanimously.
If the leaders fail to act within a year, a group of countries constituting at least a third of member-states would be allowed to introduce the measure themselves under the "enhanced co-operation" procedure.
Europe's more integrationist countries, including France and Germany, believe that enhanced co-operation, which allows groups of countries to co-operate more closely within EU structures, will be crucial in ensuring that the process of integration does not stagnate.
The new presidency draft offers a boost to enhanced co-operation by reinstating a provision that would allow groups of countries to agree unanimously to reach decisions on certain policy areas by qualified majority, without the approval of countries outside the group.
The presidency offers no comfort to those who want a reference to God or Christianity in the constitution's preamble. A note to delegations said it was not possible to find agreement in favour of such a reference.
"Despite the strong support of several delegations for the inclusion of a specific reference to Europe's Christian or Judeo-Christian heritage, there is no sign of consensus on this matter," it says.
The draft contains a declaration on the Stability and Growth Pact, committing the EU to budget discipline, price stability and promoting economic growth.
Foreign ministers will discuss the new draft this morning and the presidency hopes to find broad agreement on most of the issues raised before Thursday's summit in Brussels.
The leaders are expected to focus on the most contentious issues of all, which include the voting system in the Council of Ministers and the size and composition of the Commission.