This is not a question of protecting wildlife but of preserving fragile sovereignty - and with it the most basic, but increasingly shaky, assumptions of post-Soviet politics.
The 'bunny' under threat is Belarus's national currency, so called because of the sprightly rabbit that hops across the one rouble note (other denominations have beavers, wolves, a lynx, a moose and a bison).
The fate of the Belarus bunny is no trivial matter. It has already helped topple the reformist government in Moscow and stirred alarm in Minsk that Belarus, having been among the first to quit the Soviet empire, may soon be the first to join the reshaped empire of a resurgent Russia.
The fuss began with an announcement at the start of the month that Moscow and Minsk would merge their monetary systems. Only a month earlier, all but bankrupt Belarus had pledged to bow to Russia in military matters, too.
'There is a time to scatter and a time to gather,' says Stanislav Bogdankevich, the peeved but philosophical chairman of Belarus's soon to be emasculated Central Bank. 'Maybe the time has come now to gather in. They destroyed the union, maybe this is the start of drawing us back together.'
Also worried is Yegor Gaidar, who cited the Belarus accord when he resigned as deputy prime minister in Moscow and set off panic in Western capitals. What bothered him was not the implications for Belarussian statehood but a fear that Russia's old instincts as an imperial power have again got the better of economic common sense.
It took only two days in December 1991 for Boris Yeltsin, Leonid Kravchuk and Stanislav Shushkevich to come up with a brief statement as dramatic as any ever issued: 'The USSR, as a subject of international law and geopolitical reality is ceasing its existence.' It was called the Belovezhskaya Pusha declaration after the venue, a hunting lodge near the Polish border, built for tsars but also popular with Nikita Krushchev and other general secretaries. Russia, Ukraine and Belarus asserted their independence and set up the Commonwealth of Independent States to manage their divorce.
Minsk, a plodding backwater even by Soviet standards, suddenly became a world capital. . A grand four-storey building on the corner of Komsomolskaya and Kirov streets was emptied of Minsk Province party officials and filled with new bureaucrats for the CIS. Committees were formed, fancy titles handed out and summits arranged. And, to everyone's suprise, the CIS survived. The past year was particularly fruitful. The lobby of the Minsk headquarters now has 12 flags, two more than before.
The pretence is thin. The real capital is Moscow, home to the institutions that matter: the Russian Central Bank, the Russian Ministry of Defence. 'The CIS is just a cover for the formation of a new Russian empire,' says Zenon Poznyak, leader of the nationalist opposition in a Belarus parliament otherwise stacked with old-style Communists trained in and nostalgic for the certainties of the Soviet Union. 'We don't need Russia. We want them out of our country, out of our lives.'
He is particularly eager to see the back of 35,000 Russian troops. They service the strategic nuclear weapons which, in stark contrast to Ukraine, Belarus has promised to give up without a fight. All Belarus has so far got by way of thanks is a six-hour stopover two weeks ago by President Bill Clinton.
Mr Poznyak's nationalism is aggressive and fiercely anti-Russian and anti-Communist. He enraged the local elite, particularly the Prime Minister, Vyacheslav Kebich, by getting the site of a Stalinist mass grave, Kuropaty, put on Mr Clinton's itinerary. He is also more than a bit paranoid. He talks of sinister conspiracies. More unsettling are demands for a Greater Belarus stretching into Russia, Poland and Lithuania.
The currency union Mr Poznyak dismisses as 'economically absurd abracadabra' and part of a plot by Moscow to 'liquidate the Belarus state'.
Few of his compatriots are so strident. Belarus is far more homogeneous - and less hotheaded - than Ukraine or the Baltic states. Nearly 80 per cent of the population is Belarussian. The government charges pounds 40 for a visa and flies a red and white Belarussian flag atop its main office bloc. But that is about as far as it goes. Lenin still stands in the courtyard and the Soviet emblem decorates the clocktower. There is no national anthem yet. The Belarus Army Song and Dance Troupe uses music - but not the words - from the old republican anthem played in Soviet times.
Stanislav Shushkevich, Belarus's nominal leader and one of three men who signed the Soviet Union into oblivion, is candid: 'We have a very conservative structure. It was created in the time of Belarussian Soviet Socialist Republic and has not changed. The nomenklatura is very strong and united.'
Just how strong is shown in parliament's response to the extradition of two Communists back to Lithuania. It yesterday voted to sack two of Mr Shuskevich's last remaining allies, the ministers of interior and security: 'I have very little power in most matters.'
With Mr Shushkevitch sidelined and a parliament dominated by Soviet-era apparatchiks on the warpath, Belarus is adrift.
Since the hunting lodge session in 1991 there have been countless, mostly meaningless, declarations of intent. But something important has changed. They were built around the fiction of equality. This time the relationship is clear: Moscow calls the shots. 'Of course we are worried,' says Mr Kebich, the pro-Russia premier. 'That is why we have to behave ourselves.'
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