Thanks, Chris. Luckiliy, I figured it out. There was a tag that defined the company logo, which was set to width 100% by 80 px high. I changed it to the exact width and height of the logo instead. Then I changed the class "ms-globalTitleArea" to 100% width by 80 px, and also the id "SearchArea's" top value to 10 px instead of - 55.
The nice thing about SharePoint designer is that it allows you to go right to the CSS properties by right clicking on a class from the master page and selecting "Follow Code Hyperlink" No need to browse or do a search; it does it all for you.