The judges also reduced fines imposed on the former president from 29 million reais (US$7.4 million) to 2.4 million (US$615,000), the estimated price of the triplex.
They also reduced a fine of 175 days – where each "day" demands a payment of five times the minimum wage – to 50.
Lula was originally sentenced to nine and a half years on charges that he accepted a seaside apartment as a bribe for helping the OAS construction company during his 2003-2010 presidency to get lucrative deals with state oil firm Petrobras.
That was increased by an appeals court in January 2018 – a decision the Superior Court of Justice panel ruled Tuesday was "excessive."
Lula's legal team said the decision was "too little but it's a start," and said it would appeal, seeking a total acquittal.
"The only result we see as compatible with this specific case is the acquittal of former president Lula because we understand... that he did not commit any crime," said one of his lawyers, Cristiano Zanin.
Lula is also appealing the second sentence of almost 13 years handed down in February for accepting renovation work by two construction companies on a farmhouse in exchange for ensuring they won contracts with Petrobras.
He has denied all the charges against him, arguing they were politically motivated with the aim of preventing him competing in elections last year that were won by Brazil's new far-right President Jair Bolsonaro.
During his election campaign, Bolsonaro said he hoped Lula would "rot in prison."
Lula's efforts to get out of jail were dealt a blow recently when the Supreme Court indefinitely delayed debate on whether a prisoner convicted of a non-violent crime should be released before the end of the appeals process, which could have potentially freed him.
Bolsonaro's victory in October's elections ended decades of center-left rule in Brazil and reduced Lula's chances of freedom.
Soon after winning, Bolsonaro named Sergio Moro, the anticorruption judge who handed Lula his first conviction, as justice minister.
"Lula is innocent, he deserves to be acquitted, but the votes for the reduction of his sentence show the level of persecution and arbitrariness to which Lula was subjected by Moro," tweeted Workers' Party (PT) president Gleisi Hoffmann.