A redesign does not mean throwing everything out. Most small business sites have something worth keeping: wording that says plainly what you do, photos that are really yours, a web address your customers already know and pages that Google already lists.
Jeff starts with the site you have now. What do you like about it, what embarrasses you, what do customers say they could not find? He keeps what is doing its job and rebuilds the rest, and the new site goes live on your own domain, so nothing your customers have saved or bookmarked stops working.
If an old page is going away, its address is pointed at the page that replaces it, so a visitor from an old link or an old search result still lands somewhere useful.