How do you keep the cat out of the baby's crib?

I am setting up my new nursery for my son, who is due in June. I have a cat who thinks that any comfortable spot is his bed. I am worried about the cat sleeping in the baby's crib once he arrives. Cat's paws are dirty and their hair can cause allergies so I don't want him in the baby room at all. I... show more I am setting up my new nursery for my son, who is due in June. I have a cat who thinks that any comfortable spot is his bed. I am worried about the cat sleeping in the baby's crib once he arrives. Cat's paws are dirty and their hair can cause allergies so I don't want him in the baby room at all. I considered getting a tall gate, but Sylvester (the cat) can jump a 5 foot wall easily. I don't want to just keep the nursery door shut either, because there could always be a reason to keep it open.

Has anyone else had this problem? What did you do?

And getting rid of the cat is NOT an option. Neither is keeping him outside. I'm looking for help with the nursery, not the cat.
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