Nikolai Petrov is a political analyst at the Carnegie Center in Moscow. He says the Black Sea Fleet has already lost its strategic importance for Russia.
"On the one hand, during the 15 years that Ukraine has existed as an independent state, the Black Sea Fleet has on the whole lost its importance as a military-strategic unit," Petrov says. "On the other hand, Ukraine has used the fleet as an instrument of pressure many times and now it does not have this kind of urgency or importance that it had at the beginning of the 1990s."
Not all analysts think along the same lines. Tatyana Stanovaya, who heads the analytical department at the Center for Political Technologies, a Moscow-based think tank, says strategic considerations play a secondary role in the Black Sea Fleet issue.
"In this case, the psychological angle is of utmost importance. If Russia is forced to move the fleet out, it will be a serious blow to Russia's image, it will discredit Russian foreign policy and it will be considered to be a serious set back in [President Vladimir] Putin's policy in Russia," Stanovaya says.
However, Stanovaya says the Ukrainian side will probably be reluctant to put the Sevastopol base issue on the table.
"Kyiv cannot link these two problems [gas and the base] in the negotiations with Gazprom. Only Yushchenko can link these topics in negotiations with Putin. So far, the [gas] negotiations haven't reached such a high level," Stanovaya says.
Some analysts have said that, in addition to raising the Black Sea Fleet issue, Ukraine could take advantage of other Russian vulnerabilities -- such as its military's reliance on two early warning radar stations, located in the Ukrainian cities of Mukacheveand Sevastopol.
The two countries also have a high level of military codependence -- something that Ukraine could use as leverage.
The Russian military still relies on the Ukrainian defense industry for spare parts and for the maintenance of equipment designed and manufactured in Ukraine during Soviet times. Such equipment includes intercontinental ballistic missiles and Antonov planes. Ukraine also supplies air-to-air missiles to Russia, gas turbine engines for some warships, and engines for almost all Russian-made helicopters.
Analyst Petrov, however, thinks it unlikely that Ukraine will exert such pressure -- as it could mean Kyiv shooting itself in the foot.
"If Ukraine stops selling to Russia its heavy-industry products, and also military equipment, without any doubt it will create problems for the Russian economy and for the Russian military complex. However, it will also create big problems for the Ukrainian economy too, as it has no other place to sell these products other than Russia," Petrov says.
Kyiv is largely dependent on Russian gas. A radical increase in prices could lead to unpredictable economic and social consequences.
Russian President Vladimir Putin said recently that Ukraine's consumption of gas at below-market prices had cost Russia $4.6 billion.
Russian gas monopoly Gazprom wants Ukraine to pay up to $250 for 1,000 cubic meters of gas compared to $50 under an existing deal. Recent talks in Moscow between the two prime ministers failed to hatch out an agreement.