You said that when you swaddle him, he falls asleep fine. Have you tried swaddling him tight in a receiving blanket and putting him to sleep like that? That was the only way my son would sleep until he was about 4 months old. It was so comforting to him, he slept great. At Target, they sell things to wrap them up in to swaddle, but my son was very small too, and it was still to big for him at like 3 months old. He would sleep anywhere if swaddled, so maybe try that if you haven't been leaving him that way already. Have you tried a boucer at all? My son had some nights that he wouldn't sleep unless he was in his bouncer, and swaddled. But then he would sleep great. We also had a bouncer that plays relaxing music, lightly vibrates, and has a back massager, and I think those things helped him too (mostly the vibrating). Does your bassinet have a vibrate option? My son loved that, and my mom actually broke the thing out of it trying to take it out, so I just set it in there with him on low, and could put it on my bed near him, or anywhere he was laying, and it soothed him a lot. I don't know if these are things you have already tried... but I hope it helps some! Good luck!