Hi H.,
We had this problem with my first baby and for us, the problem was that she was too cold. Poor thing went through a week of only sleeping 15 minutes or so in her bassinet (next to my bed) and then would start fussing. I'd think she was hungry so I'd nurse her and she'd fall asleep if I held her. I now know it was my body warmth that she wanted.
She was "cured" of her fussiness when we turned up the heat, swaddled her, put a blanket over her and put her in a sleep positioner. This was all on the same night that I made these changes (after a very rough night of basically being up until 5 a.m.). We also started making her last feeding of the night a bottle of formula. This way, daddy got to do it, we knew she was full, and it gave me an opportunity to pump and build up my milk supply in the freezer.
That first night that I made all those changes, she slept for 8 hours straight! I woke up panicked that something had happened to her. :)
Anyway, don't know if that is the answer for you, but it certainly helped me.
Enjoy your new little one!