Best way to address both your wishes is to install Otto’s PHP Code Widget, and then, in one or more of those widgets, use the template tag, wp_list_categories(), with the exclude= parameter.
Thanks MichaelH, I actually ended up using these instructions:
http://www.lancelhoff.com/2008/07/19/exclude-categories-from-sidebar-in-wordpress-26/
I’m not sure how that will affect me when I upgrade my version of wp, but we shall see.
Thanks MichaelH for that simple but beautiful solution! And thanks Otto for thee plugin:-)