Named peril vs All risk Insurance

[Kirby Nichols]

We're looking for new insurance as we close on our second property. (woohoo!) Pretty much every one in our local meet up uses the same guy and is very happy with him. He almost exclusively uses "Named Peril" insurance for investment properties. It sounds like it could save us a ton, but I'm concerned about the "unnamed" risks that I may be signing up for unwittingly.

For reference, we would go with the most comprehensive policy specifically because it covers theft and leaks from plumbing. We would also have a separate umbrella policy to cover Landlord liability, and we always require proof of Renter's Insurance with our name on the policy (so we're notified if the policy lapses). So I'm not worried about those things. Also, I'm ok with taking some risk to save money, especially if it's something more within our control. For example, it looks like "infestation" isn't covered, but we do regular pest control. So an "infestation" would likely be renter liability.

Has anyone had an unpleasant surprise that something wasn't covered by their "named peril" policy?