How do I control select button width?

How do I control select button width?

Hi!
I've got some dynamically generated drop down lists in my web app.
My problem is that a select button is really narrow, so almost every list item has a  shortened name and I've got plenty of space left.
I've noticed that after the select widget gets enhanced jQuery generates some divs and an "a" element. I can set this "a" element wider, and this button really gets wider, but I have no idea how to do this programatically (I've done that through my browser's developer tools so far). This element have just normal button classes attached so I can't overload them without messing every other button on my site.
Oh, and I should probably note that this select button is placed in the header of the page.
If I didn't make myself clear (sorry for that, English isn't my first language) I attach a picture saying pretty straigthforward what I want.



Any ideas how to do that?