You defintely need padding underneath to make it comfortable for baby, and what is not usually very apparent in these shots but is absolutely necessary is that there's support cloths / padding tucked around baby to make a little 'nest'. I use rolled up cloth nappies or hand towels - just the right size, quick and easy to put in place and mould around. This helps the baby feel secure (and thus more settled) and stops a degree of rolling and movement. It also helps position baby's head to ensure it can't roll around too freely (dangerous for the underdeveloped neck muscles). There should still be a hand on baby all the time except when taking the actual shot in case it startles. I usually go for an assistant with hand on baby just gently touching / hovering over then it's '1, 2, 3' move hand, click shutter, replace hand.
Try to ensure you're using soft light which falls down the face along the line of the nose, and swaddle nice and tight - loose wrapping is something I often get wrong, you really can make it tighter than you think and it not only improves the look of the image but also helps keep baby feeling nice and snug and restricts movement.
Also try to avoid shooting 'up the nose' - this is never a good look! If anything, overcompensate and shoot down the face.
Hope this helps,
Regards
Jim