I started a new website project. I have not connected that to a server yet, I just want to work on the layout.
When I open the new project, with a new name, the files from my other project just show up there. I don't want them there- this is a completely different project. How do I do it?

Not sure if this is your exact issue, but you might try setting the CC HTML Editor so that it will not open the last-edited files when it starts up. To do this, open Tools, Preferences, and set the Application Startup to No Open Document as shown in the screenshot below:

http://www.morgus.com/cc_images/cleanstarthtmled.jpg

Another thing to check is that you not only give it a new name but you also point it to a different folder as well.

Thanks, Chuck. All is well in the preferences section
I'll look at your suggestion soon, Scott. I'm not sure how folder pointing is designated when I start a new project. I'll let ya know what happens.

Ok, got it. Thanks!