WPF Popup: How to put a border around the popup?

I've got a Popup in my XAML to show some information. When the box pops up, it has no Border and appears to blend into the Background of the page. It just needs a Border, and ideally a drop-shadow behind it to show some sort of layering and focus.

Any ideas how to style a Popup to have a border and possibly the shadow-effect?