Identity Theft & Bank Correspondence

I saw something recently that suggested that we should place any bank corresondence that contained the customer's account number in plain envelopes with no bank logo. Are any of you considering this practice? While I think it is a good idea, it may cause people to throw their statements in the trash.

Several years ago at trust school I roomed with a fellow whose bank sent statements in plain brown envelopes without even a return address, but he was from the Bahamas...

Just a personal opinion, but I don't think mail thieves sort the mail when they steal it - they just take it all. Removing your bank name and logo might be a subtle indication that you strive for customer privacy. However, as you note, many people, myself included, sort the mail with a shredder between their knees. If it doesn't look like something I want, zzzzzpppptttt, unopened.