But, accusing the regional authorities of pressuring potential court witnesses, they say they are resigned that two other ongoing lawsuits will be found in their favor.
The one court ruling invalidated the election results at the No. 426 precinct in the village of Novoandrosovka, said Nikolai Ivanov, secretary of the Kursk branch of the Communist Party. The court found that 104 ballots of the 610 votes cast had been tampered with.
"Zyuganov would have won if those ballots were not spoiled," Ivanov said in a telephone interview, adding that the Communist candidate had received 95 of the 104 changed ballots.
Zyuganov did win a majority in four precincts of Kursk. The heads of two of those districts, Zheleznogorsk and Kurchatov, were fired by Kursk regional Governor Alexander Rutskoi - supposedly for reasons other than the vote - shortly after the elections.
"Of course the official reason for the firing of those two was different from the real reason and you will never be able to prove the real reason," said Ivan Zhukov, the acting head of the Kursk regional parliament and the founder of the local branch of the Agrarian Party.
The leadership of the other two districts, Shchigrovo and Manturovo, has remained in place. Ivanov said the Shchigrovo and Manturovo leaders had been elected into office, while the two who had been sacked had been appointed by Rutskoi.
Courts are still reviewing the other two Communist cases, including a complaint filed against Rutskoi accusing him of forcing the region's residents to vote for Vladimir Putin.
"Rutskoi in televised speeches ordered people to vote for Putin and was blaming Zyuganov of all possible sins," Ivanov said.
The Communists say they are fighting an uphill battle with those suits because witnesses are increasingly reluctant to testify.
"Our problem is that when we started to go to court, many witnesses backed away from their earlier testimonies," Ivanov said. "Tremendous pressure has been put on them."
Zhukov said that pressure went back even before the elections.
"The pressure was huge, enormous, gigantic," he said. "I just don't have words to describe its scale."
Zhukov said regional government officials had held routine talks with the heads of companies and farms to discuss the vote.
"Staff from the governor's office regularly went to the districts and worked there for days preparing the electorate," he said.
"We were not invited to those meetings, but many district administration heads called us and told us about what was happening," he added. "They were told what percentage of the votes must be cast for Putin."
Zhukov declined to give further details and would not name any of the regional heads, saying that most of them had been appointed by the governor and could lose their jobs.
The Kursk Communist Party newspaper Golos Naroda (The Voice of People) wrote in a recent editorial that pressure from the governor's office had led to blackmail and threats on the electorate.
"We are positive that the results of the elections would have been different if the electorate had not blackmailed, threatened and pressured," the newspaper said. "Unfortunately, some district administration leaders and other officials gave in to the threats and did their best to make people vote for Putin, fearing that if they did not their districts would be deprived of loans, discounts on machinery and fuel, and that they could lose their own posts."
However, Zhukov said he does not believe that the initiative to pressure the electorate had come from the Kremlin.
"Of course it was from Rutskoi, who wanted to show his loyalty," he said. "But by doing this, he has made it worse for Putin."