B737 CREW TURNED IN RPTS DESCRIBING A PLT'S DISCRETION DSCNT WHICH WAS INTERRUPTED BY THE CTLR WHEN HE REALIZED OPPOSING TFC WOULD CONFLICT.

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FLT XYZ; LAS-LAX; APPROX XA55 AT FL310. FO PF. ATC GAVE US A CLRNC WHICH WE UNDERSTOOD TO BE DSND AT PLT'S DISCRETION TO FL240. ATC THEN INSTRUCTED US; TO THE BEST OF OUR RECOLLECTION; TO DSND NOW TO FL280 WITH DISCRETION TO CONTINUE TO FL240. AT APPROX FL277 ATC ADVISED US TO MAINTAIN FL280 AND TO CALL ATC UPON LNDG. ATC LATER ADVISED US THAT WE HAD BEEN TOLD TO DSND TO FL280 AND THAT WE HAD LOST SEPARATION WITH ANOTHER ACFT. SUPPLEMENTAL INFO FROM ACN 449041: I BEGAN A CAPTURE DSCNT (1000 FPM). A FEW MINS AFTER; THE CTLR REVISED THE CLRNC TO READ 'DSND NOW TO MAINTAIN FL280; WITH THE DISCRETION' THE CAPT AND I TALKED ABOUT PUTTING FL280 IN THE ALT BOX; BUT SINCE I WAS ON A CAPTURE PROFILE; AND NEAR THE TOP OF DSCNT POINT; WE ELECTED TO KEEP FL240 IN THE BOX. ATC TOLD US ABOUT TFC AT 12 O'CLOCK AT FL270; OPPOSITE DIRECTION; WHICH WE HAD IN SIGHT. I REALIZED THAT THE TFC MIGHT CAUSE A TA; SO I STOPPED THE DSCNT AT FL277 AND WAS GOING TO WAIT UNTIL THE ACFT PASSED BEFORE CONTINUING THE DSCNT. ATC HURRIEDLY CAME ON AND TOLD US TO MAINTAIN FL280; TO WHICH THE CAPT RESPONDED THAT WE WOULD CLB BACK TO FL280. HE QUERIED THE CTLR ABOUT THE PLT'S DISCRETION TO FL240 AND GOT NO RESPONSE. THE CAPT TALKED TO THE SUPVR; WHO CLAIMED WE VIOLATED OUR CLRNC BY 500 FT AND HAD A LOSS OF SEPARATION. THE CTLR ISSUED US A CLRNC THAT CAUSED A CONFLICT AND TRIED TO REVISE IT AS WE PASSED THE ALT HE MEANT TO HAVE US REMAIN AT. HE SHOULD HAVE CAUGHT HIS MISTAKE WHEN THE CAPT READ THE AMENDED CLRNC BACK TO HIM. I BELIEVE THIS STRESSES THE IMPORTANCE OF CTLRS PAYING MORE ATTN TO PLT READBACKS TO MAKE SURE THE PLTS GET THE CLRNC CORRECT; BUT ALSO TO MAKE SURE THEY ARE GIVING SAFE AND LEGAL CLRNCS.