If I sent them an advertisement to all clients who have decided to recieve the newsletter, and at the bottom put - "If you do not want to recieve any more advertisements, please reply with 'remove'" - would that be can-spam compliant?
"Newsletter" usually does mean the "news" about what we want to sell you. I think as long as there is a true, working, remove function it is probably technically legal. I think you should be prepared to do a manual remove in response to any remove request to any of your business addresses. People are generally taught that "remove" functions are scams unless you absolutely remember how you subscribed yourself to this sender. Technically I don't think the law requires the list to be opt-in, but you'll get a lot of angry responses, many to your upstream provider, if you take advantage of that loophole. Also if you subcontract your mailing list to a mass mailer, people are going to get upset about seeing stuff come from a domain other than the one they remember having opted into.