pita question

Well that's an interesting change. Usually people want to know how to get the dough to puff up well so they do have a pocket.

I've never tried to get the pita to not puff but I can tell you the way to get it to puff is by allowing a 15 minute rest time after rolling out the dough. So the reverse procedure would be to bake on a hot stone immediately after rolling out into shape. I think you might need to adjust the baking time since it is a more dense dough without further rising.

Eric

What about pricking it a few times before baking to let the air that would be puffing it, escape?

Yep, the traditional approach is to roll them thicker and to probably bake at lower temperatures. You'll get laffa that's great for shawarmas or just as a general-purpose sandwich wrap.

Prickling's probably also fine, but thick rolling's better if you still want some small air puffs in there.

You can also make them over a stove top if you want more control over the baking.

Half the fun is watching them puff as they bake :)

Once they're out of the oven they will collapse. When they've cooled I store in ziploc bags and cut into triangles and toast them, rarely do I try and open up to use the pocket. You could give that a try...

It seems as though you've gotten some good answers.

I've been making a lot of pita and flat bread lately for an Egyptian friend who is off her feet til the new bundle arrives.

Here's an excerpt from The Complete Middle East Cookbook, by T. Mallos, for flat bread without a pocket:

"Do not rest bread after shaping, and prick with a fork or pinwheel. Bake on a hot griddle or baking sheet for 4 minutes, pressing bread with a cloth if it looks as though a pocket is forming. Turn to brown other side after 2 minutes or brown under grill after baking." Flatbreads and Flavors by Jeffrey Alford has a recipe for lavash that gives directions for flat (pocketless) bread. It's pliable if baked right, not like the crackers.

I cook my flat breads (lafahs) on top of an inverted, lightly oiled wok over a gas burner. They are perfect for falafels but I think you'll find pitas are better suited for dips. 

Google homemade pita chips and you'll find lots of recipes.

Judy

I usually make the pita breads as usual, with puffing. Once they've cooled, I cut them into two full-moon halves. Then I brush them with some olive oil and za'atar and put them back in the oven to crisp up. It makes delicious, dippable chips.

I use Pitas for dipping often and that's a great recipe. I didn't know I should let them sit to get a better puff so I have been just rolling them and slapping them right in the oven, so that won't keep them flat because I almost always get a nice puff so I would just prick it with a fork.  Thanks though to ehanner for the tip about letting them rest.

Shannon

forgive my lack of knowledge, but wouldnt a non puffed pitta be more like a naan bread?

Naans, as far as I'm aware, tend to bubble, rather than puff like pittas. Almost like a pitta gone wrong. they seem to be thicker too (maybe thats why they dont puff)