New parents Jessica Alba and Cash Warren are banning their baby daughter from chasing fame - until she's at least 21.

The newlyweds are determined to make sure Honor, who was born in June, should finish her education before she pursues the life of a celebrity - if that is the life she chooses.

Alba says, "When she finishes college, she can do whatever she wants."

But the actress admits it could be tough convincing Honor to wait: "I think at some point all little kids express that desire, because they're so used to being treated like a star."