Customize category query in widget

Question

I would like to exclude a category from my categories sidebar widget. If I understand the way this works, the sidebar.php code is not in use since the widget is displaying the categories. (something similar was discussed in this support topic: http://wordpress.org/support/topic/problem-trying-to-hide-a-category-in-the-sidebar ).

How can I modify the query used by the widget; or is there another means of excluding specific categories from inclusion in the category list?