Probably won't help you (unless a CBA customer) but a warning about CommInsure.
I moved from my broker-supplied, QBE H&C policy to CommInsure two years ago as the premium was very attractive (I am a CBA 'Wealth package' customer) and the coverage was if not the same, then slightly better.
On the first renewal, the premium went up 20%. Suspecting a 'bait and switch' I complained and vigorously went after them for the reasons for the large increase. They raise insured amounts by 6% every year as standard (you can vary this) - this is above the CPI for building and contents type replacement. After much correspondence, CommInsure eventually revealed that 11% of the increase was because of the introduction that year of 'local risk pricing' (ie bushfire, storm, flood, past claims consideration based on the postcode). Mollified by a modest '1 off' premium discount, I renewed.
This year - another 20% increase. I got pretty peeved off and again pursued them for the reason / components of the increase. This time they dug their heels in and refused to give any details beyond the 6% increase in insured values. The simply pointed to the PDS which basically says they can do what they like price-wise. They did offer me a quite large 'one off' premium discount this time, but I still went back to my broker and renewed with QBE and sent a note to my 'personal banker' with the reasons. There have been no events in my postcode in the past year that would justify a +10% premium increase based on local risk pricing, so absent any reason given by CommInsure, I can only assume that its a straight premium hike, going to CBA's bottom line.
I will be making a complaint to the FIO as I still believe I was subject to 'bait and switch' pricing.