Applying Stroke to Image

Related question: I want to apply a stroke to the outside of an image (a logo) so that when I placed it over the top of another image it stands out. However, I can't figure out how to do it.

First, I was hoping for a way to apply a stroke/outline only to the outer perimeter of the logo as a whole (not to every vector segment!). I hoped that grouping everything first would do the trick. It didn't.

After giving up on that, I decided to duplicate the logo and apply the stroke to it as before, then move it behind the unedited logo, so that only the outer stroke would appear. However, the stroke applied to the bounding box! (Who intends to apply a stroke to a bounding box?!) Is there anyway to place a stroke on the entirety of an image WITHOUT stroking the bounding box? (Even when hiding the bounding box, the stroke still appears.)

I've Googled this and not found an answer.

TIA!