Liabilty insurance for rental property (Tokyo)

Can anyone tell me what they have done about the need for liability insurance when moving into a rental property in Japan? I understand why landlords would want you to have such insurance but the offer from the insurance company that our relocation agents have put us in touch with is very confusing and they don't seem able to explain it further for us. It seems to be covering a very low amount to cover accidental damage to neighbouring houses - not to mention coverage for our own belongings - an amount that might cover our bed and kitchenware but nothing else.

Can anyone recommend a decent insurance company? Can anyone explain different types of cover and what to be on the look out for?

Thanks
Sanne