A B757-200 FLT AT FL410 IS ISSUED A CLRNC TO FL350 WHICH WAS INTENDED FOR ANOTHER COMPANY FLT WHOSE NUMBER WAS NOT SIMILAR TO FLT X. ZKC; MO.

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CTLR TOLD US (FLT CCH) TO DSND TO FL350. CAPT (PNF) ACKNOWLEDGED AND I SET FL350 IN ALT WINDOW. BOTH OF US POINTED TO FL350. I BEGAN 1000 FPM DSCNT. AT FL400 THE CTLR (FREQ 125.72) ASKED US TO CONFIRM WE WERE LEVEL AT FL410. I REPLIED; 'NO; WE ARE DSNDING TO FL350 PER YOUR INSTRUCTIONS.' THE CTLR SAID WE TOOK A CLRNC FOR ANOTHER ACFT; AND I BEGAN A CLB TO FL410. I THINK HE MEANT TO GIVE THE CLRNC TO FLT EFB WHO HE HAD TO CALL SEVERAL TIMES TO GIVE A DSCNT TO. SHORTLY THEREAFTER; THERE WAS A CHANGE OF CTLRS ON THIS FREQ; AND THE CAPT ASKED HIM IF WE WERE IN TROUBLE. THE CTLR GAVE A VAGUE ANSWER THAT THE LAST CTLR GAVE A DSCNT CLRNC TO THE WRONG ACFT (OR SOMETHING TO THAT EFFECT). WE GOT THE DSCNT CLRNC 380 MI FROM DEST. IT IS COMMON ON THIS ARR (AND ALL CVG ARRS) TO DSND AS MUCH AS 200 MI BEFORE FMS TOP OF DSCNT. WE WERE GIVEN 7 DSCNT CLRNCS PRIOR TO BEING CLRED TO CROSS TARNE AT 11000 FT. WE CAN GO TO NYC AND GET 2 XING RESTRS OR GO TO LAX AND HE CLRED TO DSND VIA THE CIVET ARR. THE WAY WE DSND INTO CVG IS RIPE FOR CTLR AND PLT MISTAKES. THERE MUST BE A BETTER WAY.