Invitation Etiquette - Of Guests

How could I word an invitation so that people don`t bring along uninvited guests?

My siblings and I are planning a surprise birthday party for our mom at a country club. We want it to be a small and intimate affair (less than 35 people total) - and we`re on a limited budget - and invited guests are limited to our mother`s siblings and close friends. However, it has been noticed at other family functions that people often bring along uninvited guests. If the invitations were addressed, "Mr. X. And Guest", Mr. X. Would bring along a guest and a son and daughter. Or if the invitations were addressed to only one individual, that person would bring a guest along.

How do we word the invitations so we can make it clear that only the invitees are invited?