Advantage kills fleas on contact, and is reported to kill 98 - 100 % of adult fleas within 24 hours of application. (italiangreyhound.org)
As for the DE, I recommend actually rubbing it into your carpets as it will kill the adult fleas on contact and if any eggs hatch, it will kill the larvae. (thebugsquad.com)
It kills fleas on contact and is supposed to be effective on your cat for one month. (myhealthycat.com)