ALTDEV ALT OVERSHOT -- DSCNT THROUGH THE CLRNC ALT BY ACR FLC.

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OUR ACFT WAS RETURNING TO MIA AT FL310. WE WERE APCHING MTH NDB FROM THE S TO JOIN THE DOLIN 2 ARR INTO MIA. WE WERE INITIALLY CLRED TO DSND TO FL200 AT PLTS DISCRETION. SOMETIME AFTER BEGINNING OUR DSCNT; WE RECEIVED CLRNC TO CONTINUE OUR DSCNT. I THOUGHT WE WERE CLRED TO DSND TO CROSS WEVER AT 14000 FT AND 250 KTS IN ACCORDANCE WITH THE ARR. HOWEVER; WE WERE CLRED ONLY TO 17000 FT. AS WE DSNDED THROUGH 17000 FT; WE RECEIVED THE AURAL SIGNAL FROM THE ALT ALERTER. AT THIS TIME I ASKED THE CAPT AND FE IF WE HAD INDEED BEEN CLRED TO 14000 FT. IN THE ABSENCE OF A CONCLUSIVE RESPONSE; I ARRESTED THE DSCNT AT APPROX 16500 FT. ALMOST SIMULTANEOUSLY ATC CLRED US TO CROSS WEVER AT 14000 FT AND 250 KTS. THE FLT CONTINUED NORMALLY FROM THIS POINT ON. I AM CONVINCED THIS ALTDEV WOULD NOT HAVE OCCURRED IF THE CREW HAD NOT BEEN SO FATIGUED. ALL 3 OF THE CREW MEMBERS HAD BEEN AWAKE FOR OVER 24 HRS. WE HAD SHOWN FOR DUTY APPROX 18 HRS PRIOR TO THE ALTDEV. THIS WAS AN INTL FLT AND THEREFORE WE WERE NOT SUBJECT TO A DUTY TIME LIMITATION. WHEN THE CREW ARRIVED AT THE ARPT FOR THE TRIP; OPS INFORMED US THAT THERE WOULD BE A SLIGHT DELAY DUE TO ACFT MAINT. AFTER APPROX 4 1/2 HRS; WE REQUESTED A REPLACEMENT CREW FOR THE TRIP. THIS REQUEST WAS DENIED AND AFTER NEARLY 6 HRS THE ACFT WAS READY. THE TRIP CONSISTED OF 4 LEGS. THERE WERE NO FACILITIES FOR CREW REST IN BTWN LEGS. ON THE FINAL LEG; ALL OF CREW REMARKED HOW TIRED WE WERE AND WE HOPED WE DID NOT HAVE TO FLY ANYWHERE ELSE UPON OUR ARR INTO MIA. WE HAD ACCUMULATED ONLY ABOUT 7 1/2 HRS OF FLT TIME AND WOULD HAVE BEEN PERFECTLY LEGAL TO FLY ANOTHER 4 1/2 HRS. WE ALL REALIZED THAT OUR PERFORMANCE WAS NOT AS SHARP AS USUAL DUE TO OUR FATIGUE WITH THE END RESULT BEING AN ALTDEV. OF COURSE; BETTER COCKPIT RESOURCE MGMNT COULD HAVE PREVENTED THIS ALTDEV. BOTH PLTS SHOULD RESPOND TO A CLRNC ALT; 1 PLT OVER THE RADIO AND THE OTHER OUT LOUD TO CONFIRM THE CLRNC AND ACKNOWLEDGE ITS RECEIPT. THE BIGGER ISSUE IS THE FATIGUE ISSUE. I BELIEVE THERE IS A REAL NEED TO ESTABLISH DUTY TIME LIMITATIONS FOR INTL FLTS.