The help message displayed in the Change Priority dialog when increasing
priority (lowering the nice value) states that root priveledges are
required to lower the nice value below 0.  What it should say is simple
that it requires root priveleges to lower the nice value.  As an example,
raise the nice of a process to 19 using the dialog.  Then lower it to 0. 
The resulting message could be a bit confusing.