I'm not and have never been in your situation but consider this a summary of all anecdotes I've heard mixed with negotiation techniques.

The thing I would personally do is make sure the client has paid their invoice before providing the service. Essentially, this means paying for all previous missed invoices along with the next one. If you make people pay before giving the service, I think you avoid the case altogether.

Now, if you want to be harder: just ban them. Take them to Collections (or whatever the name is in the USA) and then never provide services to them ever again. This sounds really harsh and unfair but by not paying they also know how far they can go without giving you a dime. "Give them a hand and they take the arm."