Thanks for the links.
At least I discovered what is causing my 'problem'.
The window must stay wide enough to display the formatting and other buttons above the text input area. So I guess the more buttons one has there, the wider the minimum width of the window will be.
So I disabled the 'Off the Record' plugin and gained the ability to reduce the width by the amount its button was taking up.
If I could find a means of getting rid of the 'Attention' and 'Insert' buttons, while retaining the 'Font' and 'Smilies' buttons, that would be more useful to me.
Thanks for the assistance.
At least now I know what causes the problem.