Place eggs in single layer under 3 inches of water in a saucepan. Bring to a boil for 7 minutes; cover, remove from heat and keep standing for 15 minutes.
Drain and place eggs in a bowl with ice water.
Gently crack eggs on the counter. Peel under cold, running water.
Cut eggs in half lengthwise and carefully remove yolks. Mix yolks with mayonnaise. Add mustard, relish, salt and pepper. Stir well.
Spoon egg yolk mixture into egg whites. Garnish with paprika, if desired. Chill and serve.