Birkhead filed a lawsuit against Smith on October 2, after her partner and
lawyer Howard K. Stern announced on TV show 'Larry King Live' that he is
Danni Lynn's father.

Smith's lawyer, Ron Rale, claimed the judge "threw out 80 percent of their case.

"This isn't nearly the end of the story," said Rale.

Smith, 39, has been residing with Stern, 38, in the Bahamas, where she gave birth to Dannielynn on Sept. 7. Three days later, her 20-year-old son Daniel died in Smith's hospital room.

The former Playboy pinup and Stern returned to the U.S. last week for a hearing in San Francisco in her effort to collect an inheritance from her late husband, oilman J. Howard Marshall II.

As they left the court, Stern was served with papers alleging he lied in
statements for the paternity suit filed by Birkhead.

Stern has been listed as the father on Danni Lynn's Bahamian birth
certificate.

Superior Court Judge Robert A. Schnider also ruled that the parties in the case will have to work out whether the tests will be done in the United States or in the Bahamas.