How to fit the width of each button to it's text on a horizontal menu?

Go to the advanced mode of the horizonal menu. Check the auto width checkbox. 
This feature allows you to fit the width of the buttons to the text on it. it is useful when you have a lot categories on a horizontal menu and you want to squeeze them. You can also align the menu to fit on the left right or center.

Here is how to fit the width of each button:

Step 1: Enter the vertical menu's edit mode

Step 2: Click advanced

Step 3: Check the 'auto width' check box (in red)

Step 4: Choose alignment left/center/right for the horizontal menu (in blue)

Note: Make sure you are on the Menu tab within General