Does the Cal.USPS have the right to deliver Un-addressed &-named junk mail, after I've asked not to?

Question

Do I have a right to decline unaddressed junk mail from the United States Postal Service?
My mailbox is constantly filled up with supermarket newspapers, vouchers and other junk mail that is either completely without address, or just says "Resident". 

I have asked the mail deliverer nicely to skip our mailbox with such advertisement, because that didn't help, I put a sign on the mailbox, saying: Please No Advertisement or Newspapers" That still didn't work, so the sign got bigger and in more vibrant colors saying. "NO Advertisement, Please only mail that has OUR names, thank you". Well, after two good weeks, now my mailbox is full to the brim again!

What is the law in California for unaddressed mail service like this? Does the USPS have the right to deliver such mail, although I specifically asked not to, or do I have any right not receive unaddressed mail?

I know that junk mail with my name on it is a whole other story and that there are opt-out lists, that sometimes help. 
But what about the mail without my name, or sometimes even completely without address?

Thank you.

Answer

The USPS is staffed by people doing a job, not always a job that you appreciate. They deliver every piece as addressed. If you want to refuse it you can, but if it's just trash mail they are going to just trash it. My post office provides a big trash can by the door for exactly that purpose.

Does the Cal.USPS have the right to deliver Un-addressed &-named junk mail, after I've asked not to?

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