Combine water, shortening, and salt in a heavy saucepan. Bring to a full boil, melting shortening completely.
Remove pan from heat and add flour all at once. Stir quickly and vigorously with a wooden spoon.
Return to heat and continue stirring vigorously until dough forms a smooth, dry ball that does not cling to the spoon or to the sides of the pan. Do not overcook or dough will not puff properly.
Transfer dough to bowl of mixer with flat beater and add eggs slowly (about 2ounces/60grams at a time), beating on medium speed after each addition. Eggs should be completely mixed in before the next portion is added. If desired, eggs can be beaten in by hand.
Continue beating mixture until all egg is absorbed. Dough should hold its shape when lifted on the end of a spoon, but it should still be smooth, moist, and workable.
Place a plain tip in pastry bag and fill bag with choux paste.