Firefox should auto-hide the Downloads button on the Navigation Toolbar by default. The Download button should appear on the Navigation Toolbar once you open the Customize window. If you do not see the Download icon then click the Restore Defaults button to reset the layout in case you previously have moved this button. Once you see the Download button in customize mode then left-click this button to see the current auto-hide state and toggle its setting.

That worked fine for the download icon. Thank you. BUT -- when I restored the defaults, I lost the Adblock Plus icon on the toolbar. It still shows as enabled in the extensions page, but the icon is gone.

Never mind. I found it in the Customize options.