Place currants in a medium-size bowl.
Cover with warm water, and set aside to plump for 5 minutes.
Preheat oven to 425°F.
Roll out half of pastry, and line a 9-inch pie plate with it.
In a medium-size saucepan, dissolve cornstarch in 1/2 cup reserved cherry juice.
Add cherries and drained currants.
Bring to a boil over medium heat, stirring constantly, until thickened, about 10 minutes.
Remove from heat, and stir in almond extract.
Turn into prepared pie plate.
Roll out remaining pastry.
Cut several steam vents into top.
Place pastry over filling and trim, crimping edges together with fingers.
Bake on middle shelf of oven for 15 minutes.
Reduce heat to 325°F, and continue to bake for about 15 minutes, or until pie is golden.