How to stop addressed junk mail largely depends on how the sender got hold of your name and address.
How did you get on the junk mail database?
Have you ever given any thought to the term direct mail? According to the industry it's any type of targeted advertising mail. When Virgin Media sends 25 milion letters addressed 'To the Occupier' it's "direct mail". Those pizza leaflets you get through the door are "direct mail". Even inserts in free newspapers are nowadays seen as "direct mail". I'd like to propose a more sensible definition. Let's call advertising mail that has been requested by the recipient solicited mail – or, if you insist, direct mail – and let's call unsolicited mail what it really is: junk mail.
The industry doesn't like terms such as unsolicited mail or junk mail. It's sounds too negative. Yet, the industry's opt-out scheme for addressed mail, the Mailing Preference Service, can only stop unsolicited mail – solicited mail would still get to you, as you'd expect. Similarly, the reason why marketeers hide opt-out boxes that can prevent adverts is so that they can send you solicited mailings (and by-pass the Mailing Preference Service).
When it comes to stopping addressed junk mail the terms solicited and unsolicited are important – but it's not always clear when addressed advertising mail is solicited. Is an advert you get because you failed to tick a hidden opt-out box really solicited, or have you simply been conned? When you register to vote and you're asked for permission to have your name and address used as a commodity, are you really opting in to something? Addressed junk mail is a bit of minefield.
Luckily, there is a very powerful tool to stop addressed junk mail: data protection notices. And for those who don't fancy sending formal notices to individual junk mailers there's always the option to send the junk mail back to the sender / offender.