Most auto insurance companies have direct repair programs and can refer you to one of their shops. The shop assesses the damage and communicates with the insurer for you."Delays are not very good for keeping customers," notes Passmore. The goal is to get each claim handled as quickly as possible, and to make sure the right amount is paid so the insurer doesn't have to deal with it again. "If insurers are going to do things like delay, they're going to lose a customer."