Place eggs in a pot of salted water. Bring the water to a boil, & let eggs cook in boiling water until they are hard boiled, approximately 10-15 minutes. Drain eggs & let cool.
Once cool, remove the shell, cut the eggs in half lengthwise & scoop out the yolks.
Place the yolks in a medium-size bowl & mash them. Blend in vinegar, mayonnaise, mustard, salt & pepper. You may need to add more mayonnaise to hold the mixture together, but it should be slightly dry.
Carefully put the egg yolk mixture back into the egg whites, but do not pack them. There will be enough mixture so the whites are overfilled.