An article at Pet Tails had more information and I was interested in what it said about stages of sleep and positions dogs sleep in. One comment was that if the dog is curled up she is probably in a light sleep. I would say this is true of Penny because if I walk past her when she is curled up she is often resting with her eyes open - I assume she opens them when she hears me moving around.
I also feel sure this article is correct when it says dogs sleep on their backs with their paws in the air because they have less fur on their bellies and thus they are trying to cool down. I've often seen Penny sleep like this on a warm night.
Animal Behavior Associates says
How much do dogs and cats sleep? Under controlled laboratory conditions both cats and dogs sleep about 13 hours per day but they wake up more frequently than people do. How much and when pets sleep varies enormously depending on the social and physical environment. A dog living as an only pet in an apartment may sleep much more than one working as a herding dog on a farm. Pets will often adjust their activity and sleep cycles so that they can be active when people and other animals are active.