Place all eggs in medium saucepan; cover with cold water. Bring to a boil, reduce heat, and cook 8 minutes. Remove pan from heat and run cold water into it until eggs feel cool to the touch.
Crack and peel eggs. Chop into bite-size pieces and place in a large mixing bowl. Add celery, onion, salt and pepper, and 3 heaping tablespoons mayonnaise. (More mayonnaise may be added if desired.) Blend well. Serve on bed of lettuce with wheat crackers, or on favorite bread as a sandwich.