Preheat oven to 400 °F (205 °C).
In a saucepan, bring to a boil water, butter, salt and sugar.
Remove from heat.
Pour in flour all at once.
With a wooden spatula, mix until well blended.
Return to heat in order to dry paste.
Mix constantly to avoid burning.
Remove from heat.
Transfer paste to a bowl.
Let cool 5 minutes, stirring occasionally.
Fold in eggs one at a time, until paste is smooth and glossy.
Using a pastry bag with a medium size fluted nozzle, squeeze 1 inch (2.5 cm) puffs or 4 x 1 inch (10 x 2.5 cm) eclairs onto a buttered cookie sheet.
Lightly brush with beaten egg.
(Do not let egg drip onto cookie sheet.) Bake in oven 25-30 minutes.
Let puffs cool fully before stuffing.