Playing nice with org-bullets

Now that org-sticky-header is working well for me, I am getting picky, so feel free to ignore this request. But, I am using org-bullets to replace org-mode's asterisk with the UTF-8 character ●. I would like for the sticky header to look the same way, so I added this to my .emacs file:

(setq-default org-sticky-header-heading-star "●")

And it looks good as long as I am in a first level header. But if I am in a second level header, an asterisk is added to the sticky header, and it looks like this:

*● My first level heading / My second level heading

It is possible to do something about it? Because I am showing the full path in the sticky header, I do not need two bullets. I would like simply not to show the asterisk.

Many thanks!