They sell a floor leveling *mortar* that can be poured over concrete.
I did the same thing you are talking about and all I had to do was put
some milky bonding chemical on the old concrete first (they sell it
right next to the leveling mix).
Make sure you have a good seal around everywhere you want to pour the
leveler, it is fairly runny at first. You should mix it all up in one
batch for one pour. The stuff does need a little help to *self-level*,
I just used and old straw broom to sweep it out a little bit.
Overall worked great and the stuff was very flat when dry. The
thickest part was about 2 inches thick and never gave us trouble for