This is one area where I'm strict because I have rugs everywhere, beige ones and a beige couch! My policy is that there must be 30 days without an accident before I will allow a child to use underpants only and I still put the pullup over the underpants for naptime. I want the children to train and will do all I can to help but once they are able to run out to the bathroom on their own and know when they have to go then I stop worrying about accidents. That usually happens after they are about 3 to 4 years old. Parents expecting a 2 year old to be that advanced are dreamers in my opinion, that's still the 'training' stage which spells accidents.