How is it possible that I can dream in 10 minute bursts?

I haven’t really read any literature recently on sleeping and dreaming, but the last time I was reading on it I thought that REM was highly correlated to dreaming, but now I am not so sure based on what happens to me.

In the morning I set my alarm for 7:30am. I have lectures at 9am, so I generally set it earlier so I have time to wake up. What I often find is that I fall asleep again and wake up 10 mins later after having a dream. This happens perhaps 2–3 times before I get up for my shower at 8:20am. I was thinking that 10 mins is too fast to go straight to REM sleep even if I was facing severe sleep deprivation. I am mostly tired, but I always get at least 6 hours sleep a night.

So does anyone have any interesting research that links to this? Or do people have their own experiences where they dream in relatively short periods of time.