FLC MISUNDERSTOOD ALT CLRNC DURING DSCNT. RESULTING IN LOSS OF SEPARATION. CTLR INTERVENED.

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WE WERE CLRED TO CROSS BECKX INTXN AT 7000 FT. BECKX INTXN IS 7 MI N OF THE SCURRY VOR ON THE 313 DEG RADIAL. I THOUGHT WE WERE CLRED TO 7000 FT AND THE PNF READ BACK CROSS BECKX AT 7000 FT; CLRED TO 6000 FT. HE PUT 6000 FT IN THE ALT ALERTER. A REGIONAL CARRIER ATR WAS BELOW US ENRTE TO SCURRY AS WELL. I HEARD HIM CLRED TO 6000 FT AS WELL. ZFW CALLED THE TFC TO US AND WE SAW HIM. HE WAS 5 MI IN FRONT OF US AND SEVERAL THOUSAND FT LOWER. WE WERE TOLD TO MAINTAIN VISUAL SEPARATION. WE READ BACK THAT WE WOULD MAINTAIN VISUAL SEPARATION. I FAILED TO HEAR WHAT THE PNF READ BACK TO ZFW ABOUT THE ALT CLRNC. AT 8000 FT I CALLED OUT '8000 FT FOR 7000 FT.' THE PNF SAID 'YES; BUT WE ARE CLRED TO 6000 FT.' I CONFIRMED THIS BY LOOKING AT THE ALT ALERTER AND 6000 FT WAS IN THERE. I FIGURED THAT I HAD GOTTEN CONFUSED WITH WHAT WE WERE CLRED TO WITH THAT OF THE ATR. AT 6200 FT SEVERAL MI S OF BECKX; CTR SAID 'LEAR XXX; SAY ALT.' THE PNF READ BACK 'XXX LEVEL 6000 FT.' CTR CAME BACK TO SAY WE WERE CLRED TO 7000 FT AND DID WE STILL HAVE THE ATR IN SIGHT. WE DID AND WE WERE CLRED BACK TO 7000 FT. CTR SAID NO PROB BECAUSE WE HAD THE REGIONAL CARRIER ACFT IN SIGHT. THE REGIONAL CARRIER ATR HAD A TCASII RA AND HE STAYED ABOVE US. THE PROB LIES WITH THE FACT THAT WE HAD BOTH BEEN UP SINCE EARLY AM AND WE WERE ON OUR 7TH LEG OF THE DAY. WE HAD BEEN DOWN TO MEXICO AND HAD A FULL DAYS WORK. I HAD ONLY 2 HRS SLEEP AND THE PNF HAD 3 HRS SLEEP THE NIGHT BEFORE. I FEEL THAT IF THE 135 REGS ON DUTY TIME ARE REWRITTEN TO ACCOUNT FOR THE TIME OF DAY A PLT STARTS DUTY TIME AND ADJUST THE MAX HE/SHE CAN BE ON DUTY THAT FLYING WOULD BE SAFER FOR ALL OF US. WE WERE WELL WITHIN OUR DUTY TIME BUT WE STARTED AT EARLY AM IN THE MORNING. WHEN PEOPLE GET TIRED PEOPLE MAKE MISTAKES. THERE ARE TOO MANY LOOP HOLES IN THE 135 DUTY REGS. THE FAA SHOULD MAKE OUR REGS MORE LIKE 121 REGS.