Sigh

SQL, our 3 month old puppy is now pooping in his crate.
It seems to happen sometime during the night after bed time. We take him out for a walk right before he goes to bed, then we lie down in bed for ten minutes, then I put him in the crate. He'll cry for ten minutes and then fall asleep.
The next morning my fiancee gets up around 5:10 and lets SQL out

Only to find poop. The crate is divided as small as possible. He's only 2 lbs, so he's really teeny.
Not sure if we should wake up at some point in the night to let him out to poop? We go to bed at 9:30 or 10:00 latest.
I know he's little and not to expect too much from him. But I don't want this to be a habit.
Any help?