APPARENT SIT IN WHICH AN ALT OF 3000 FT WAS ISSUED WHICH CAUSED THE FLC TO LEVEL AT 5000 FT AFTER RECEIVING A BRIEF GPWS WARNING AS THE CTLR TOLD THEM TO STOP DSCNT. CTLR THEN RECLRED THEM TO MAINTAIN 5000 FT.

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DURING DSCNT INTO SWF; WE WERE CLRED TO 7000 FT AND HANDED OFF TO APCH. THEY SUBSEQUENTLY CLRED US TO 3000 FT AND TOLD US TO EXPECT A VISUAL APCH TO RWY 27 AND TO CALL THE FIELD IN SIGHT. READ BACK 3000 FT AND TOLD APCH WE WERE STILL IN THE CLOUDS WITH MODERATE CHOP BUT WOULD LOOK FOR THE FIELD. SHORTLY THEREAFTER; WE HEARD A XMISSION WITHOUT A CALL SIGN. THEN APCH CALLED US AND TOLD US TO STOP OUR DSCNT JUST AS WE SIMULTANEOUSLY BROKE OUT OF THE CLOUDS AND GOT A VERY SHORT TERRAIN WARNING ON THE GPWS. WE TOLD APCH THAT WE HAD STOPPED OUR DSCNT AT 5000 FT AND HE TOLD US TO MAINTAIN THAT AND ASKED US IF HE HAD CLRED US TO I BELIEVE IT WAS 5000 FT. WE TOLD HIM WE HAD BEEN CLRED TO 3000 FT AND HE TOLD US TO MAINTAIN 5000 FT. THE REST OF THE APCH WAS UNEVENTFUL. SUBSEQUENT REVIEW REVEALED THAT THERE WAS A QUADRANT IN THAT AREA WITH A MINIMUM SECTOR ALT OF 4900 FT. CONTRIBUTING FACTORS COULD HAVE BEEN THE CHOP AND AN EARLY MORNING WAKE-UP; BUT OBVIOUSLY WE SHOULD HAVE MAINTAINED A BETTER AWARENESS OF THE OBSTACLES IN THE AREA THAT WOULD HAVE PREVENTED THIS FROM OCCURRING.