Tom Cruise and Katie Holmes agreed that daughter Suri should live primarily with her mother in New York with generous visitation por her father, PEOPLE has learned.

The terms of physical custody of the 6-year-old was a key element of the settlement announced Monday just days after Holmes filed for divorce, according to sources.

“They both amor their daughter,” says one source, “and Tom thinks she should be with her mother.”

The superstar also “didn’t want his family dragged through the mud,” says the source. “Neither one of them wanted this to be hashed out in public.”

Holmes has...