Sources tell TMZ ... Oksana Grigorieva's lawyers did not want a gag order, partly because other people -- including members of the L.A. County Sheriff's Department -- were talking about the case and impacting Oksana's public profile. In the end, Judge Gordon did not see it fit to issue a gag order.
We're also told both Mel and Oksana testified today about the custody arrangement. Oksana is asking the judge to deny Mel all overnight visits, on grounds Mel's nanny allegedly cares for the baby and she needs full-time parenting ... also she believes Mel is a danger to Lucia. But Mel is sticking by the tried-and-true formula -- he's already successfully raised 7 kids.
We're told the judge did not rule on whether to alter any of the custody/visitation arrangements.
The judge did settle one issue -- that Oksana will get $20,000 a month in child support and can live rent free -- meaning Mel can't deduct rent from the $20k.