Spot on, Len. For anyone, like myself, who's just getting into the business and thinking about getting a website together, you have to be very careful when dealing with web designers.
Firstly, make sure they understand the business, as most are excellent designers, but they ain't businessmen. Most importantly though, is that you insist from day one that they document the fact that, although they create the site, you want copyright.
The way it stands at the moment (and I don't think it will change in the foreseeable future) is that in the case of a dispute, the law will recognise the designer as holding copyright and not the client, even though you may have paid big bucks for it. The other important thing to note is that if the designer retains copyright, he will almost certainly be the only person with accesss to make amendments, so insist on having some level of administrator rights to amend the site yourself. It can get mighty expensive if you have to go back to him each time you want to change a word or paragraph here or there.
Sorry if it's a case of 'teaching your grandmother to suck eggs' for those with established websites, but as this thread was started by someone looking to set up a site for the first time, I thought it might be worth mentioning.