Prepare and roll out pastry for single-crust pie. Line a 9-inch pie plate with the pasty. Trim and crimp edges as desired.
For filling combine eggs, corn syrup, butter, sugar, and rum. Mix well; stir in walnuts or pecan halves.
Place in pastry-lined pie plate on the oven rack. Carefully pout the filling into pastry shell.
To prevent overbrowning, cover edge of the pie with foil. Bake in 350 degree F oven for 25 minutes. Remove foil. Bake for 15 to 20 minutes more until a knife inserted near the center comes out clean. Cover and refrigerate within 2 hours.