Our carseat has head support which was needed as she'd flop around too much otherwise. The support can be removed, so I have took some of it out when she started sit up. I also found the padding in the seat helped her to actually fit in the seat properly too.

With the pram, we didnt have a head support in the pram to begin with. I did end up getting one form another BB member. It was one of those U shaped pillows that you can put the pram straps through and it was great. The pram was quite large so as a tiny newborn she'd just roll around and end up sideways as the straps didnt do up tight enough to actually hold her in place. The U shaped thing helped to just hold her in the one spot and she looked more comfortable with it.