Slime? When I had my 'ped, I used it AND the old tires. Here's what I did:
1. Fill the new inner tubes with the recommened amount of slime.
2. Take old tubes, cut off the stem, cut in half.
3. Straighten cut tube and cut so that the tube can be laid out flat.
4. Place old, cut tube inside tire and lay new, slimed, tube inside the old tube.
5. Install tire as normal, keeping the old tube between the new tube and the actual tire.
NEVER got a flat.