I still like to do a Dawn wash just before putting on additional coats of Zaino (to make sure I strip off any road oils) but a quality auto shampoo should do just fine.

The first Dawn wash is to remove any previous wax-based products that you or the dealer used on your paintwork.

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Congrats on your budding steps into auto detailing. With any abrasive material, remember to start with the LEAST abrasive material... rub a bit (5 seconds w/ medium pressure)... clear it away... examine carefully. If 2 or 3 rounds of this doesn't fix your problem, you can then move to something slightly more abrasive.