EU members offer conflicting remedies: Britain and Denmark want a broad Europe with loose links, while Germany and France urge deeper integration.
There will be a tough fight at the summit over who will be president of the European Commission when Jacques Delors retires in January after 10 years. Gearing up for battle are the hot favourites, Belgium's Prime Minister, Jean-Luc Dehaene, and the outgoing Dutch Prime Minister, Ruud Lubbers. The EU Trade Commissioner, Sir Leon Brittan, lobbying furiously, has an outside chance.
The 12 leaders will sign a partnership deal with President Boris Yeltsin, promising stronger political and trade ties. On Wednesday, just in time for the summit, Russia's Foreign Minister, Andrei Kozyrev, visits Brussels to sign Nato's Partnership for Peace, which offers closer military links with the West.
This is expected to ease tension between Nato and Russia over Russian demands for special ties reflecting its status as a major power. Nato insists that a broader relationship will be limited and that Moscow certainly cannot have a veto. But, as a concession to Russia's size and weight, Nato has offered Russia further talks on nuclear arms and Bosnia.
Russia will be keeping a beady eye on presidential elections in Ukraine on Sunday and Belarus on Thursday. Moscow fears that a strong nationalist signal from Kiev could blow off-course delicate talks on dividing up the Black Sea Fleet and stir up separatist feelings in the predominantly Russian Crimea. Leonid Kuchma is Moscow's choice, but the nationalist Leonid Kravchuk is gaining ground in the polls.
In Belarus, the pro-Moscow candidate Vyacheslav Kebich, a former Soviet-era apparatchik who is strongly tipped to win, promises to take the republic into the rouble zone and hand over financial powers to the Russian central bank.
Germany and Switzerland will be pressing competing claims to host the new World Trade Organisation on Thursday and Friday. The Swiss see no reason to move the trade watchdog - the successor to Gatt - from Geneva and will resist Bonn's application. Each will argue its case before the WTO's budget, finance and administration sub-committee, which will try to reach a consensus. Insiders back Geneva.
The Dutch Supreme Court rules tomorrow on whether a doctor may help a healthy patient to commit suicide.