RH,
"Special handling" PERM applications are processed much faster than the regular PERM applications. LC special handling applications should normally be processed within 2-4 weeks from the time that they are filed unlike regular PERM applications which normally take 4 to 12 weeks. Bear in mind that processing time is subject to change and if DOL decides to audit in either case, it might take longer.
HowardRoark,
For any classification, be it regular or Master's, one must be fully qualified on the date of filing the petition. This means that you should have your diploma in hand when you file. You can submit the letter from your school confirming completion of all coursework except for the actual degree along with the petition BUT there are more chances that it will be denied.
Thanks Sa54