How do I paint over peeling paint?

I have steamed off a border in my bedroom and the result was chunks of paint peeling off with the border. This is not all over the walls but big chunks here and there.
Is there any product I can use to seal the ends of this peeling paint and so it doesn't look so noticable when I put on the final coat of paint and will leave the wall with a smooth even finish?
thanks
lou, March 2010


done
To Do It Right
1.you need to sand it with a 220 fine paper til smooth
2.then wash with a damp soap and water rag with mild dishsoap [ no bleach in soap]
3.wait til dry then wip with a dry rag
4.then prime paint
5.then re-paint

tHE PAINT DOCTOR, October 2010
Hi there is paint peeling above my front door, everytime we paint over it, it makes it worse how do we deal with this problem as it looks unsightly.

donna, April 2010
The reason for the paint peeling off, was that the plaster surface wasn't primed properly when the first coat was applied. Your best bet is to rub down the rough edges of the paint, clean the dust off and prime the bare surface with a 50/50 mix of emulsion paint and water. If using oil based paint use a primer coat first, thinned 50/50 with white spirit or turps. This thin mix will prime the surface ready to take the next coat or two. You will still probably be able to see where the original coat came off the wall though.

Homer, March 2010