Hmm, you want to exploit my imagination! Ok:
a) Mr. Brown, you said you fell back asleep at 9 am, exactly when your wife was found dead. What did you do this morining, before falling back asleep?
b) Lemme think. Before falling asleep... hmmm. I read for over an hour before falling back asleep. And I also called my daughter after reading. Nothing else.
I read for over an hour this morning, then fell back asleep. <--- this wouldn't work in the above context.
In other words, I wanted to say that:
I read for over an hour this morning, then fell back asleep. <-- you fell asleep right after you'd read for an hour
I read for over an hour this morning before falling back asleep. <-- something else might have happened between reading and falling asleep.
In most contexts they would have exaclty the same meaning, though.
Now remember I'm not a native speaker, so you might want to wait for some natives, since I could have written nonsense.