B737-300 CREW LOST CTL OF CABIN PRESSURIZATION IN ZTL CLASS A AIRSPACE.

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SLOW DEPRESSURIZATION OF CABIN. DEPARTED RDU AND CLBED TO FL350. AFTER ABOUT 15 MINS AT FL350 THE ACFT BEGAN TO DEPRESSURIZE. THE CABIN ALT AURAL WARNING SOUNDED AT ABOUT 10000 FT CABIN ALT. IMMEDIATE CLRNC WAS RECEIVED TO DSND TO FL240. PASSING FL300; CLRNC WAS GIVEN TO 11000 FT. DSCNT WAS RAPID WITH SPD BRAKES UP BUT WAS NOT UNCOMFORTABLE. DSNDING THROUGH ABOUT 16000 FT; THE PAX OXYGEN MASKS DEPLOYED. PAX HAD BEEN BRIEFED AFTER DSCNT STABILIZED. ACFT LEVELED AT 11000 FT; PRESSURE DIFFERENTIAL WAS APPROX 1.0 PSI GIVING A CABIN ALT OF ABOUT 8000 FT. COORDINATED WITH DISPATCH AND ATC AND PROCEEDED TO MDW AT 11000 FT. APCH AND LNDG AT MDW WAS UNEVENTFUL. SUPPLEMENTAL INFO FROM ACN 556360: FLT WAS OUR FIRST OF THE DAY FROM RDU-MDW. APPROX 15-20 MINS AFTER LEVELOFF AT FL350; THE CABIN ALT WARNING HORN SOUNDED. CAPT COORDINATED AN IMMEDIATE DSCNT AND STARTED DOWN. I PULLED OUT THE QRH AT THAT TIME. WE DSNDED ALL THE WAY TO 11000 FT WHERE THE CABIN ALT STABILIZED AT 8000 FT. THE OXYGEN MASKS IN THE CABIN DEPLOYED AT SOME POINT IN THE DSCNT. THE DEPRESSURIZATION WAS NOT RAPID AT ALL. THE CAPT TALKED TO THE PAX AND COORDINATED WITH THE FLT ATTENDANTS TO MAKE SURE EVERYONE WAS OK. AFTER SOME DIFFICULTY CONTACTING DISPATCH; WE MADE THE DECISION (AT DISPATCH'S REQUEST) TO CONTINUE TO MDW. THE REMAINDER OF THE FLT WAS UNEVENTFUL. ON AUG/THU/02; I RECEIVED A CALL FROM CHIEF PT. HE TOLD ME THE FAA WANTED MY CERTIFICATE NUMBER AS A RESULT OF THE FLT. AFTER READING THE CAPT'S IRREGULARITY RPT; THE CHIEF SAID THE ONLY POSSIBLE CONCERN HE COULD SEE WAS THAT WE DID NOT DECLARE AN EMER. HE SUGGESTED WE FILL OUT AN ASAP RPT BASED ON BEING NOTIFIED OF FAA ACTION ON AUG/THU/02. I BELIEVE WE HANDLED THE SIT PROPERLY AND A DECLARATION OF AN EMER WAS NOT WARRANTED. WE IMMEDIATELY ASKED FOR AND RECEIVED DSCNT CLRNC; THEN REQUIRED NO FURTHER ASSISTANCE. FOM GUIDANCE IS NOT CLR OR SPECIFIC ON WHETHER AN EMER SHOULD BE DECLARED IN A SIT LIKE WE ENCOUNTERED.