Stir the lukewarm water, yeast, and sugar together. If using active dry yeast, let the mixture stand for 5–10 minutes until foamy; instant yeast may be mixed directly with the flour.

Add the flour, salt, and olive oil, then mix until a shaggy dough forms. Knead by hand for 8–10 minutes or with a dough hook for 5–6 minutes, until smooth, elastic, and slightly tacky.

Place the dough in a lightly oiled bowl, turn it once to coat, and cover. Let it rise in a warm place for about 1–1 1/2 hours, or until doubled in size.

Divide the risen dough into 8 equal pieces of approximately 80–85 g each. Shape each piece into a smooth ball, cover, and rest for 15–20 minutes.

Roll each ball into a 6–7-inch round that is approximately 1/8–1/4 inch thick. Avoid pressing the outer edges excessively, since an even thickness helps the pita inflate.

Heat a baking stone, steel, or inverted heavy baking sheet in a 475–500°F oven for at least 30 minutes. The cooking surface must be thoroughly hot before the first pita goes in.

Bake one or two pitas at a time for about 2–4 minutes, watching for full inflation and light brown spots. Remove them promptly so they stay soft instead of becoming crisp.

Wrap the baked pitas in a clean towel while they cool. The trapped warmth keeps the bread pliable and protects the delicate pocket.