Put smoke alarms on every floor, and make sure the agent knows about them. A smoke alarm may not only save a life, it will pay for itself in a year or two with the 2 percent or so that it will save you on premiums. Ask for all possible discounts.
Some companies offer discounts.
If so, it should cost less to insure. You might be eligible for a price break. If you normally keep some of your gems in a safe deposit box, and if they're worth more than the standard policy limits, ask if you would be eligible for a break on the cost of a rider. See if you can get a multiple policy discount. You might need to accept less coverage for the contents of your second home, or to install an alarm system to detect trouble before the pipes freeze.