Will they or won't they? Lawyers for CHRISTIE BRINKLEY and PETER COOK met at a hearing this morning in New York Supreme Court to discuss whether or not their divorce trial will be open to the public and the press. Lawyers for news media also had an opportunity to file motions for or against the notion. The hearing is done for the day.

Upon exiting the courtroom this morning, Cook said he's "Waiting for a very smart judge to make a decision." When a reporter asked him to respond to "Christie's argument that justice requires this case to be open to the press," he laughed.

Exiting after Cook, Christie said to reporters, "I've always hoped to be able to settle these matters privately, outside of the courtroom, and I continue to hope that that will be the case."

According to Newsday, law guardian THERESA A. MARI was expected to argue today that the former supermodel's two younger children would be harmed by press exposure to certain facts of the case, which may begin as early as next month.

The custody, visitation rights and child support of the couple's two young children, SAILOR, 9, and JACK, 12, are at stake. Jack, who was adopted by Cook, is Brinkley's son from her previous marriage to RICHARD TAUBMAN. Brinkley also has a 22-year-old daughter, ALEXA RAY JOEL, with first husband BILLY JOEL.

After a decade of marriage, Brinkley filed for divorce from Cook after she learned that he was having an alleged affair with his 18-year-old assistant, DIANA BIANCHI, in the summer of 2006.