As the trial opened before a jury in U.S. District Court in Manhattan, Judge Jed Rakoff set narrow parameters for what can be discussed.
Also precluded is any talk of an investigation by then-New York Attorney General Eliot Spitzer and a parallel probe by American International Group Inc (AIG.N: Quote, Profile, Research, Stock Buzz) that resulted in Greenberg's ouster as CEO in 2005.
AIG's suit against Greenberg-controlled Starr International centers on a large block of AIG shares held by Starr. The stock was once valued at $20 billion but is now worth far less since AIG shares have tumbled over the last year.
AIG, claiming breach of fiduciary duty, is seeking to wrest back shares held by Starr and the proceeds of any sales, at the same time as it tries to repay $85 billion in taxpayer bailout funds.
Rakoff said he would exclude any discussion of AIG's taxpayer bailout or bonuses because its relevance to the case was "dubious in the extreme and prejudice clear."
Bonuses paid to executives of an AIG financial products unit responsible for a significant portion of the company's $100 billion in losses over the past year caused nationwide outrage earlier this year.
The U.S. government stepped in to save AIG from collapse under bad mortgage bets last September, and has put up to $180 billion at the company's disposal since then.
AIG has promised to use any funds won at the trial to repay U.S. taxpayers. Before the government bailout, Starr was AIG's biggest shareholder.
Starr's ownership of AIG stock has been in contention since Greenberg left AIG. Starr held about 290 million shares at the time.
Starr had held a sizable stake in AIG since 1970, when Greenberg structured the firm as a vehicle to protect the insurer from hostile takeover.
After jury selection, Ted Wells of the law firm Paul, Weiss, Rifkind is expected to make opening statements for AIG, arguing that Starr, under Greenberg's direction, established a trust in 1970 for the purpose of holding the block of shares expressly to fund deferred compensation for AIG's top employees.
David Boies, of Boies, Schiller & Flexner, representing Starr, is expected to argue that Greenberg used the stock to fund deferred compensation for AIG employees on a voluntary basis, and never expressly committed to continue the program indefinitely.
Starr ceased to be a compensation vehicle for AIG executives in 2005. It is now run by Greenberg as a private investment vehicle and for charity.
Greenberg, 84, was in the courtroom on Monday morning but ducked out as proceedings got underway. He is expected to be called as a witness by AIG as early as Tuesday.