Unfortunately for me, if I fall asleep in the middle of the day, I am going to sleep for 2-3 hours, sometimes longer. Sleeping for less than that is pointless; it can sometimes take me at least 15-20 minutes to get to sleep. And, I'm not sleep-deprived; I get plenty of rest these days, having already burned my body out on all-nighters coding in elementary, middle and high school. I can't do it anymore.
The refreshing effect even from a very short period of sleep (think nodding off at a lecture) can be surprisingly strong. Try going for a nap and setting an alarm clock to go off after 20 minutes, without any expectation to necessarily fall asleep in the time. I often find that 20 minute daytime naps help a lot even if it seems to take more than 10 minutes for me to start nodding off.
