My agent warned me that AIG (now Chartis...) had a terrible administrative department, but it really is appalling. When I've needed to add coverage, the amendment (and a new bill!) is sent almost immediately. When i reduce coverage, however, it's a struggle to get them to send an amendment, and then it takes them months to reflect the reduced premium in the billing. On my latest bill, the clerks who applied the payment applied it in the wrong proportion on the various policies, and i just received a cancellation notice because of underpayment on one of the policies (they didn't bother to see that another had been overpaid!).
Unless you have hours to spare dealing with an agent who then deals with the company, save yourself some aggravation and use a company that a) has decent administration and b) lets you talk to them directly.