Yes, you can adjust the minimum width of the Dragon SideBar by altering a particular .ini file within Dragon NaturallySpeaking v11.
It is VERY IMPORTANT that have an experienced computer technician perform this custom configuration becuase it is very easy to corrupt your installation of Dragon NaturallySpeaking.  Please contact a Certified Dragon Dealer to perform any changes to the Dragon .ini files.
The minimum SideBar width is set by a number that exists in nssystem.ini, a file whose location depends on your Operating System. 
Windows XP C:Documents and SettingsAll UsersApplicationDataNuanceNaturallySpeaking11
Windows Vista – C:UsersAll UsersNuanceNaturallySpeaking11
Windows 7 –  C:ProgramDataNuanceNaturallySpeaking11
1. Close Dragon NaturallySpeaking v11
2. Open the nssystem.ini file in Notepad.
3. Look for the lineenx sample commands min width= and replace the number after = with a smaller number, like 100.
4. Save and close the file.
Verification Source: In-house testing