Mix flour, salt, and sugar together. Add butter and shortening, lightly tossing in flour to prevent the pieces from sticking together as your adding it. Cut shortening and butter into flour with pastry blender until they are about the size of peas.
Combine vinegar and ice water. Slowly drizzle over flour mixture, 1 tablespoon at a time, mixing lightly with a fork between tablespoons, just until dough can be pressed together without falling apart. The dough shouldn't be sticky and there shouldn't be excess water at the bottom of the bowl.
Knead dough on a lightly floured surface, just until dough is smooth and holds together but not enough to warm the dough or fully incorporate butter/shortening into flour. This will give you a dough that is easy to roll out but not tough and chewy.
Shape dough into 6" round disks. Wrap in plastic wrap and put in refrigerator for at least 1 hour but up to a day to chill through.
On a lightly floured surface, roll out dough 2" wider than pie plate for bottom crust. Start by pressing down the floured rolling pin into dough, gently pressing in both directions. Then roll to desired dimensions. Cook according to pie directions.
Notes
If making dough for a savory meal, such as pot pie or quiche, the sugar can be omitted.