LESS THAN STANDARD SEPARATION BETWEEN TWO ACR ACFT. OPERATIONAL ERROR.

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ON DSCNT INTO MCI WE WERE CLRD TO DSND TO 13000' AND HELD THERE DUE TO DEPARTING TFC. WHILE WE WERE LEVEL AT 13000' ZKC POINTED OUT TFC AT OUR 11 O'CLOCK POSITION. A SHORT TIME LATER KANSAS CITY AGAIN POINTED OUT TFC AT OUR 11 O'CLOCK AND IN THE SAME SENTENCE SAID WHAT WE UNDERSTOOD WAS CLRD TO 12000'. I READ BACK 'OUR IDENT; DOWN TO 12000' WITH NO FURTHER COMMENTS FROM THE CTLR. WE STARTED A DSCNT AND AT ABOUT 12300-12400' KANSAS CITY ASKED US WHAT WE WERE DOING. I TOLD HIM WE WERE DSNDING TO 12000' AND HE SAID HE HAD NOT CLRD US OUT OF 13000'. I THEN TOLD HIM HE HAD CLRD US TO 12000' AND THAT I HAD READ IT BACK TO HIM AND HE DID NOT SAY ANYTHING TO US. AT THAT TIME THE DISCUSSION STOPPED AND HE CLRD US TO 10000' SINCE THE TFC WAS NO LONGER A FACTOR. THE CAPT DID TALK TO KANSAS CITY BY PHONE AT MCI; HOWEVER; NOTHING WAS RESOLVED. ON THE NEXT DAY THE CAPT TALKED TO KANSAS CITY AGAIN. BY THIS TIME KANSAS CITY HAD REVIEWED THEIR TAPES AND THEY TOLD MY CAPT THAT WE HAD READ BACK THAT WE WERE CLRD TO 12000' AND THAT THE CTLR HAD FAILED TO CORRECT US. THEY DID NOT SAY WHAT THE CTLR'S EXACT INSTRUCTIONS WERE; BUT IT SEEMS THAT HE WAS TRYING TO TELL US THAT THE TFC WAS AT 11 O'CLOCK AT 12000 AND WE MISUNDERSTOOD HIM TO CLEAR US TO 12000'. OF NOTE; WE DID HAVE THE TFC IN SIGHT FROM THE TIME IT WAS FIRST POINTED OUT UNTIL IT PASSED OFF OUR LEFT WING AND A MIDAIR WAS NEVER A POSSIBILITY. ALSO; WE DID HAVE AN FAA AIR TFC CTLR RIDING OUR JUMPSEAT AND WAS LISTENING TO THE RADIOS. HE TOLD US THAT HE UNDERSTOOD THE SAME CLRNC TO 12000. MISCOM OR MISUNDERSTOOD COMMUNICATIONS WAS THE PROBLEM HERE. TWO THINGS CAN BE DONE TO PREVENT THIS SITUATION. AS CREWMEMBERS; WE CAN READ BACK THE DEPARTING ALT AND THE CLRD ALT; ESPECIALLY; WHEN ALT CHANGES TAKE PLACE AROUND CONFLICTING TFC. THE CTLR CAN POINT OUT TFC BY GIVING HIS POSITION AND ALT AND TELLING THE ACFT TO 'MAINTAIN' A PARTICULAR ALT I.E.; TFC AT 11 O'CLOCK AT 12000 MAINTAIN 13000. SUPPLEMENTAL INFO FROM ACN 87604: APPARENTLY HE MEANT OUR TFC WAS AT 12000' BUT WE UNDERSTOOD HIM TO MEAN WE WERE CLRD TO 12000'. HOW DID IT HAPPEN? I FEEL WE MISUNDERSTOOD THE CTLR AND HE DIDN'T CATCH IT WHEN WE READ BACK OUR MISUNDERSTANDING. HAD HE SAID 'THE TFC IS AT 12000 MAINTAIN 13000' AND HAD WE STATED 'LEAVING 13000' FOR 12000''; MAYBE WE COULD HAVE PREVENTED IT. CLEAR COMMUNICATIONS ARE STILL OUR BIGGEST PROBLEM.