Think I mentioned elsewhere that I sometimes just rip up and compost some of these things. I don't think anyone will be raiding my compost bin for financial stuff.
Also I will cut out portions of the necessary info--name, address, any numbers that look like any sort of tracking. I might cut that into smaller pieces and drop into different trash cans that will get taken out on different days. This makes me feel paranoid.
Then I can recycle or compost the very largest protion of the papers.
In reality, I hardly ever get CC advertisements. I think that's due to my zip code.