Hi, please see under the heading 'Turn search suggestions on or off' in Change your default search settings in Firefox.

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search sugestions are gone now, but the search with box is still there ...

Firefox 34 restructured the search bar to have those "one-off" search buttons you can click to run the query on a different site than your default search site.

As far as I know, there's no built-in setting to suppress that part of the panel. However:

• There is a temporary way to switch back to the search box of Firefox 33 and earlier (details at the end).

• Many parts of Firefox's user interface can be modified using custom style rules, and applied using either the Stylish extension or a userChrome.css file. I haven't seen a rule for this, but someone could try to write one for you, or if you search on the following site, you might find one: https://userstyles.org/

To switch back to the old search bar (this may not exist in future versions of Firefox):

(1) In a new tab, type or paste about:config in the address bar and press Enter. Click the button promising to be careful.

(2) In the search box that appears above the list, type or paste search and pause while the list is filtered

(3) Double-click the browser.search.showOneOffButtons preference to switch it from true to false

This doesn't affect the current window, but each new window you open (Ctrl+n) will have the old Search bar.

You can consider to move the search bar to the "3-bar" menu button drop-down list via Customization mode or via the right-click context menu of the magnifier icon (Move to Menu).