Using a horizontal orientation is a good option. Or else if you need the same vertical plot, you can also try the following
Axes tab -> Change Primary dimension Labels to Vertical ( | ) or Inclined ( / )
Presentation Tab -> limiting the number of visible bars (Max Visible Number) and using X axis scroll bar
Not sure if you Dimension values are still bigger ..
Personally, I think this is a shortcoming of the application. I'm always being asked to "display the full labels"... which is a chore. It irks me to consider saying "no" to something as basic as that.
However, I've used something like the following as the expression of a dimension:
=if(Len([FieldName])>30,Left([FieldName],30) & '-' & Chr(10) & Right([FieldName],Len([FieldName])-30),[FieldName])
Essentially, this will look for field names > 30 characters.
If it's > 30, it splits the line @ the 30th character (using the Chr(10)) , adds a hyphen, and displays the remainder of the text on the line below. If it's < 30, it displays the whole field name.
Obviously you can change the number of characters from 30 to fit your own chart's size.
It's crude, but it works well enough in most instances.
If you come up with any better ideas, please let me know!
(I suspect there could be a way of counting the characters in a string, and counting the number of spaces in a string, then performing the split at one of those spaces so that you don't get single/orphan characters on the second line...but if the application just had a few more fundamental and improved display options, we wouldn't have to even consider it!)