We considered this, but have some features coming that will need the space.
#1: I suggest that we shrink the navbar in width to about the width of the longest item ("Questions" in this case).
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I want it because the button I most frequently will be "Questions". Hence, I will only use 25% of the bar, so I want thing I will use rarely to take up as little space as possible. And I don't want to do 2 clicks to get there.
#2: Make sidebar position: fixed; for quicker access
Currently when we scroll to the bottom of the page and the horizontal bar is sticky I can "refresh" questions section by making a single click on "Questions" in navbar:
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But the new sidebar gets hidden on scroll down and now we are no longer a single click away from the "Questions" section, but position: fixed can fix that:
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And when both changes above are applied, together with the suggestion about grey background from another answer, we get small, convenient sidebar:
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#3: Replace sidebar text with icons
We considered this approach but it is very hard to find icons that are easily identifiable to a large majority of people.
... or we could make such an option available to be toggled in user preferences.
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This will further improve allocation of space.
