Consider cork underlayment. It is pretty thick (about 5/8") and has some insulation value. It is installed quite often in condos due to its soundproofing qualities. It can be installed over your floor with standard carpet adhesive using a 1/8 v-notch glue trowel and it cuts easy with a razor knife.
You will have to call around to locate it (tile supply warehouse is a good start.)
The drawbacks- You cannot install vinyl flooring over it. Opt for tile flooring.