For each individual omelet, break eggs into a small bowl and add salt, pepper, and water.
Beat just enough to mix yolks and whites.
Heat an omelet pan (or a 7 or 8-inch frying pan with sloping sides) over medium-high heat; melt butter, and tilt pan to coat bottom and sides.
Pour in egg mixture and cook, gently lifting cooked portion to allow uncooked portion to flow underneath.
Gently shake pan to keep omelet free.
Continue to shake pan and lift omelet edges until there is no more liquid but the top still looks moist and creamy.
Spoon 2 or 3 tablespoons filling down center of omelet, in line with pan handle.
Fold omelet in thirds.