> I feel like the white background makes the tooltip harder to distinguish from the document paper which is also white.

I 100% agree, and suggested a black background, not white. :) In particular was thinking of something that looks like 
![KDE tooltip](http://4.bp.blogspot.com/-LyhA1rRs8ng/T8s9I9CBaBI/AAAAAAAACBE/npkGm0OYPVg/s1600/tooltips-4.9.0.png)

My primary issue is with having both a border and a shadow. Since a shadow does seem very desirable here, it being a popup, we should get rid of the border.