ACR FLC INTERPS ZKC CLRNC; DSNDING TO A PREVIOUSLY ASSIGNED ALT; CONFLICTING WITH ANOTHER ACFT.

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FLT FILED TO FL370 ON CLBOUT OF OKC. ADVISED THE RIDES ABOVE FL260 WERE BUMPY OVER TULSA; SO WE (ACFT X) LEVELED AT FL250. FL250 WAS BUMPY OVER TULSA; SO ON FREQ CHANGE; WE ADVISED ZKC AND THEY OFFERED US FL240. WE CRUISED FL240. NEXT FREQ CHANGE; WE WERE GIVEN A DSCNT TO 16000 FT. I ASKED IF IT WAS OUR DISCRETION. CTR SAID 'DSND TO FL230; THEN DSND TO 16000 FT.' A FEW MINS LATER; CTR SAID 'DSND TO FL190 FOR TFC.' WE THOUGHT THE TFC WAS BTWN FL190 AND FL230; SO WE EXPEDITED OUR DSCNT TO FL200; THEN SLOWED TO APPROX 1000 FPM AS TO REACH 16000 FT ON OUR DSCNT SCHEDULE. AT FL187; CTR ASKED OUR LAST ASSIGNED ALT. WE REPLIED 16000 FT. CTR HAD NO REPLY. ON FREQ CHANGE TO STL APCH; WE ASKED CTR IF THERE WAS A PROB BACK THERE. CTR REPLIED WE LOST SEPARATION; TFC AT FL180; 4 MI. DON'T WORRY ABOUT IT; IT'S OK. FURTHER FOLLOW-UP WITH A PHONE CALL FINDS A POSSIBLE PLTDEV BEING CHKED BY THE QUALITY ASSURANCE PEOPLE. FURTHER FOLLOW-UP SHOWS NO PLTDEV; IMPROPER PHRASEOLOGY. NEXT TIME I WILL ASK WHERE THE TFC IS AND/OR IF WE STILL HAVE A DSCNT TO THE LOWER PREVIOUSLY ASSIGNED ALT.