what I sometimes do, and learned to do it from the guys over at ZAINO is the following...
wash the car with some sort of dish soap...dawn is what I use
then clay the whole car with a lubricant
then polish however you feel like doing so
then wax
then quick detail
then clean up the trim and treat it because the dawn is pretty drying and it will affect the look of the trim after so many times washing with dawn and no treatment to protect it
then stand back and look over your work and be satisfied, or upset that it didnt come out perfect and fix what you dont like about it....
the dawn is said to stripall polishes and waxes off the clearcoat, but not harming the clearcoat at all....then the clay removes the above surface contaminant, and a cleaner wax will remove the below surface contaminants. That is what I have been told, and it works for me....some cars I dont do it, some I do (dawn)