How to completely stop "oven spring"?

Toast

I think it's called "oven spring." Sorry... I'm a newbie to *real* bread making beyond simple rolls and bread.

Anyway, I've tried to make animal shaped rolls like this with my sourdough sandwich bread recipe: http://www.thejc.com/lifestyle/recipes/61930/recipe-cheesy-animal-bread-rolls

Problem is that the dough rises so much in the oven that the animals end up misshapen and bloated. Is there a way to prevent this?

Should I "overrise" the dough before I even shape it? I mean... sourdough yeast eventually eats up all the food and stops rising, right? I've noticed that if I sometimes leave the loaf too long in the final rise that it actually deflates a bit in the oven when I bake it. So is that the way to do it?

Or is something like this impossible with sourdough because it's so finicky?

Let the rising and baking puff them out?    

Or try reducing dough hydration to the minimum when mixing up the dough.  Leave out some of the water.

Are you wanting to eat them or just for decoration, if decoration then a dead dough or a dough with no yeast is the way to go this is what is used for decorative pieces  or else use only a small amount of yeast and get a small amount of rise. 

regards Derek