A B737-300 FLT CREW PERFORMED A RAPID DSCNT FOLLOWING A SLOW CABIN PRESSURIZATION LOSS WITH A WARNING HORN. AN EMER WAS NOT DECLARED.

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APPROX 40 MINUTES INTO OUR FLT AT 35000 FT; THE CABIN ALT WARNING HORN WENT OFF. LOOKING UP AT THE PRESSURIZATION PANEL AND CABIN ALT PANEL ALL SWITCHES WERE IN THE CORRECT POSITIONS. THE CABIN ALT WAS 10500 FT AND CLBING. I DETERMINED THE ACFT WAS LOSING PRESSURIZATION AT ABOUT 2000 FPM. I ASKED THE CAPT TO GET US A DSCNT LOWER. ATC IMMEDIATELY ANSWERED WITH A DSCNT FROM 35000 FT TO 24000 FT. THE CAPT AND I DONNED OUR OXYGEN AND ESTABLISHED COMMUNICATIONS. ONCE THIS WAS COMPLETE I EXTENDED THE SPD BRAKES AND STARTED A DSCNT ON OR CLOSE TO VMMO/MMO. THE CAPT ESTABLISHED COMMUNICATIONS WITH THE FLT ATTENDANTS. AFTER STARTING THE DSCNT I COULD STILL SEE THE CABIN CLBING AT ABOUT 2000 FPM. I ASKED THE CAPT FOR LOWER AND HANDED HIM THE QRH. ATC INITIALLY GAVE US 24000 FT; THEN WE ASKED FOR LOWER AND WE GOT 12000 FT. HE WENT THROUGH THE CHKLIST ITEMS WHILE I CONCENTRATED ON THE DSCNT. WE CONSIDERED DECLARING AN EMER BUT AT THE TIME WE WERE IN THE MID-TEENS ON OUR WAY DOWN AND IT SEEMED LIKE THE EMER WAS OVER. I BELIEVE THAT THE CABIN ALT MADE IT UP TO 16000 FT BEFORE THE ACFT DSCNT EQUALIZED THE PRESSURE. PASSING SOMEWHERE THROUGH THE TEENS; I STARTED LOOKING FOR THE CLOSEST COMPANY CITY. WE HAD NO DELAYS IN OUR DSCNT ALL THE WAY DOWN TO 12000 FT. AFTER A BRIEF CALL TO ATC; ZZZ1 WAS DETERMINED TO BE THE CLOSEST FIELD AND A VECTOR WAS ASSIGNED 180 DEGS FROM OUR CURRENT COURSE BACK TO ZZZ. I ASKED THE CAPT FOR BELOW 10000 FT AND HE GOT US 9000 FT DIRECT TO ZZZ. I SENT AN ACARS MESSAGE TO DISPATCH ABOUT A DIVERSION FOR PRESSURIZATION. THE CAPT COORDINATED WITH THE FLT ATTENDANTS. ALONG THE WAY DOWN I EXCEEDED SOME OF OUR ALT RESTRICTIONS IN AN EFFORT TO GET THE CABIN BELOW 10000 FT. ALL CHKLIST ITEMS WERE COMPLETED AND ALL NORMAL CHKLIST ITEMS WERE COMPLETED ON OUR SHORT FLT TO ZZZ. WE LANDED FROM A VISUAL APCH UNEVENTFULLY. AFTER TOUCHDOWN; THE CABIN STARTED TO PRESSURIZE BELOW SEA LEVEL. BOTH THE CAPT AND I COULD FEEL A LARGE PRESSURE DIFFERENTIAL. WHILE APCHING THE GATE; I SHUT DOWN THE LEVEL. ONCE THE ACFT WAS PARKED; I HAD TO OPEN MY WINDOW TO BREAK THE PRESSURE SEAL. I THINK WE STARTED DOWN THE RIGHT PATH WITH THE EMER BUT GOT SIDETRACKED INTO NOT DECLARING AN EMER. AS WITH ANY REAL TIME EMER; CREW COORDINATION COULD HAVE BEEN BETTER. BUT OVERALL; I THINK THIS SITUATION WAS HANDLED IN A PROFESSIONAL SAFE WAY.CALLBACK CONVERSATION WITH RPTR 705505 REVEALED THE FOLLOWING INFO: RPTR STATED THAT OTHER THAN THE DOOR SEAL FAILING; MAINT DID NOT IDENTIFY ANY OTHER FAILED COMPONENT.SUPPLEMENTAL INFO FROM 705507: AT FL350 CRUISE; THE ALT WARNING HORN SOUNDED AND THE CABIN PRESSURIZATION APPEARED TO BE STABLE AT 10000 FT. ALL OTHER INDICATIONS WERE NORMAL. WE REQUESTED AND RECEIVED DSCNTS TO FL240; 12000 FT AND FINALLY 9000 FT. I THOUGHT INITIALLY THIS WOULD BE PRECAUTIONARY ONLY. WE DONNED OUR OXYGEN MASKS AND ESTABLISHED COMMUNICATIONS. IN AN APPROX 3000 FT TO 4000 FT DSCNT AND AROUND 18000 FT MSL; I TALKED TO THE 'A' FLT ATTENDANT AND ASKED IF THE MASKS DROPPED IN THE BACK. SHE SAID THEY HAD AND I SAW THAT THE CABIN ALT WAS NOW 14000 FT. WE HAD ACCOMPLISHED THE CABIN ALT WARNING HORN/ABNORMAL PRESSURIZATION CHKLIST WITH NO CHANGE IN THE SYSTEM. WE COORDINATED WITH ATC TO LAND AT THE NEAREST SUITABLE FIELD. WE WERE UNABLE TO COMMUNICATE WITH DISPATCH ON FREQ AND WE NEVER HEARD FROM THEM WHEN WE ASKED OPS TO ASK THEM TO COME UP TO FREQ. THE FO ACAR'D THEM AND RECEIVED THE RESPONSE; 'DID THE MASKS DROP' AND 'DID YOU DECLARE AN EMER?' EVERYTHING WAS STABLE AT 9000 FT; THE FLT ATTENDANTS SAID THE CUSTOMERS WERE OK; SO WE ACAR'D 'YES AND NO.' I INTERVIEWED THE OPS AGENT WHO HAD TALKED TO THE PAX. THE PAX WERE OK. I INTERVIEWED THE FLT ATTENDANTS AND; OTHER THAN SOME SINUS STRESS; THEY WERE READY TO GO. EVERYBODY WAS LOADED; THE RELEASE WX WAS GOOD AND I ASSUMED WE COULD WORK IT OUT LATER. SO WE LAUNCHED FOR OUR DEST AND HAD THE THREE-WAY THERE AND FINISHED THE DAY IN ANOTHER CITY. I DID NOT SEE THE QUICK RISE IN CABIN ALT WHEN WE GOTTHE CLRNC TO FL240; 12000 FT AND 9000 FT. I SHOULD HAVE DECLARED AN EMER. I THOUGHT IT WAS SLOWLY RISING. THE CHKLIST WAS ACCOMPLISHED LIKE AN EMER; SO EVEN IF ATC HAD ALREADY GIVEN US EVERYTHING AS QUICKLY AS WE COULD DO IT AND THE PAX WERE OK AS PER MY CHECK WITH THEM; DECLARING AN EMER AND CANCELING IT LATER WITH NO RUSH WOULD HAVE BEEN BETTER. I SHOULD NOT HAVE DEPARTED WITHOUT TALKING WITH A CHIEF PLT AND DISPATCH. I TRIED; THEN GOT DISTRACTED IN A GO MODE AND I THOUGHT I COULD COMPLETE IT LATER.CALLBACK CONVERSATION WITH RPTR 705507 REVEALED THE FOLLOWING INFO: CAPT STATED THAT THIS CREW HAD NO DIFFICULTY IDENTIFYING THE CABIN ALT WARNING HORN BECAUSE EACH HAD JUST COMPLETED A TRAINING SESSION THAT INCLUDED A PRESSURIZATION PROB. WHAT WAS DISCONCERTING FOR THEM WAS LACK OF SECONDARY INDICATIONS ON THE PRESSURIZATION CTLR. THERE WAS NO 'AUTO FAIL' OR 'STBY ON' LIGHT. AFTER THE ACFT WAS ON THE GND; THE CREW HAD TROUBLE DEPRESSURIZING THE ACFT AND CONSIDERED CLOSING THE BLEEDS AND SHUTTING DOWN THE ENGS. IN THE END; OPENING THE FO'S WINDOW DEPRESSURIZED THE ACFT. MAINT SAID THE CTLR MALFUNCTIONED AND ALSO THE FWD CARGO DOOR SEAL WAS LEAKING.