Put 1 cup lukewarm water in a large mixing bowl. Add yeast and sugar. Stir to dissolve. Add the whole-wheat flour and 1/4 cup all-purpose flour and whisk together.
Put bowl in a warm place, uncovered, until mixture is frothy and bubbling, about 15 minutes.
Add salt, olive oil and nearly all remaining all-purpose flour (reserve 1/2 cup). With a wooden spoon, stir until mixture starts to come together in a mass.
Dust with a little reserved flour, then knead in bowl for 1 minute, incorporating any bits of dry dough.
Turn dough onto work surface.
Knead lightly for 2 minutes, until smooth.
Cover and let rest 10 minutes, then knead again for 2 minutes.
Try not to add too much reserved flour; the dough should be soft and a bit moist.
Clean the mixing bowl, oil it and put dough back in it. Cover bowl tightly with plastic wrap, then cover with a towel. Put bowl in a warm place.
Leave until dough has doubled in size, about 1 hour.
Place a baking stone in the oven and heat oven to 475 degrees.
Punch down dough and divide into 8 pieces of equal size. Form each piece into a little ball.
Place dough balls on work surface, cover with a damp towel and leave for 10 minutes.
Remove 1 ball (keeping others covered) and with a rolling pin, roll into a flat disc about a 6" circle. Repeat for the remaining dough.
Carefully lift the dough circle and place quickly on hot stone. Put as many will fit on your stone.
After 2 minutes the dough should be nicely puffed.
Turn over with tongs or spatula and bake 1 minute more.
The pita should be pale, with only a few brown specks.
Transfer warm pita into a cloth and cover so bread stays soft.
Repeat with the rest of the dough balls.