My daughter wasnt a preemie but she was an awful sleeper. She had severe acid reflux so she was constantly screaming and puking, I actually thought I'd lose my mind with the lack of sleep. I seemed to be permanently close to tears. She started sleeping through around 5 months I think when it improved a bit. Hopefully that isn't the case for you though. She sleeps much better now, doc reckons if she hadnt had that reflux she would've been a great sleeper. I was so jealous of my friends whose babies started sleeping through from 8 weeks on. Hope it gets better for you mamma, I will never forget those nights!