AN ACR FREIGHTER FLT DSNDS BELOW THE INITIAL APCH ALT OF 2650 FT WHILE MAKING A NIGHT BACK COURSE APCH INTO COU; MO.

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ON JUN/TUE/98; I JUMP SEATED TO JFK AND SLEPT IN A HOTEL FROM XA30 PM TO YE30 PM AND ACTED AS COPLT ON FLT JFK TO ILN AND SLEPT IN LOUNGE CHAIR FROM XL00 UNTIL XN00. DEPARTED AS COPLT (PNF) ON FLT ILN TO COU. CAPT WAS 'NODDING' OFF FROM TIME TO TIME. HE COMMUTED FROM MISSISSIPPI TO FLY THE TRIP. HE ELECTED TO FLY THE BACK COURSE LOC APCH BECAUSE OF A TAILWIND ON THE OPPOSITE RWY. WE WERE VECTORED TO A TURN ON FINAL AT 3000 FT MSL; INTERCEPTED FINAL APCH COURSE THEN BEGAN A DSCNT TO FINAL APCH MINIMUMS. A VISUAL DSCNT POINT OF 1.2 DME AND A GEAR DOWN POINT AT 8 DME. ACFT WAS CONFIGURED AT SLATS EXTEND; FLAPS 15 DEGS AND DSCNT TO 2650 FT (FINAL APCH FIX ALT) WAS COMMENCED. I MADE CTAF CALLS OF OUR POS AND NOTICED; AT ABOUT 10 DME; THE ACFT'S ALT WAS AT ABOUT 2450 FT AND DSNDING WHEN THE ALT ALERTER (SET TO 2650 FT) WENT OFF. THE CAPT BEGAN A CORRECTION WHEN APCH ADVISED 'LOW ALT ALERT CHK ALT.' THE CAPT CLBED BACK TO 2650 FT AND WE COMPLETED THE APCH AND LNDG. WE WERE BOTH TIRED. I HAVE PRIDED MYSELF AS HAVING BEEN A GOOD SUPPORT PLT; SOMEHOW I DROPPED THE BALL AND HAVE TRIED TO REMEMBER WHAT I WAS DOING WHEN WE WERE DSNDING FROM 3000 FT TO 2650 FT AND BELOW -- I CAN'T. THE CAPT MENTIONED THAT WHEN THE ALT ALERTER WENT OFF HE THOUGHT THAT IT WAS BECAUSE I HAD NOT RESET IT FROM THE 3000 FT SETTING TO FINAL APCH FIX ALT. WHEN FLYING ON THE 'BACKSIDE OF THE CLOCK;' WE FIGHT SUBTLE INCAPACITY BY MAKING THE CALLS; WE MADE THE CALLS AND RESET THE ALERTER -- IT WASN'T ENOUGH THIS TIME -- THIS HAS NOT HAPPENED TO ME IN THE PAST.