ALT OVERSHOOT AS THE RESULT OF MISUNDERSTANDING OF CLRNC AND READBACK CORRECTION.

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AFTER DSCNT FROM FL330 TO FL240; THE CTLR ISSUED A CLRNC FOR THE ARR. I READ BACK; 'DSND TO 150 AND INTERCEPT THE 300 DEG RADIAL TO CWK' AND ASKED HIM TO REPEAT THE INTERCEPT HDG. HE SAID THAT WAS HDG 150 DEGS (IN HINDSIGHT HE WAS CORRECTING MY INTERP OF THE '150'). I THOUGHT THE HDG WAS IN CONJUNCTION WITH FLT LEVEL 15000 FT. WE TURNED TO HDG 150 DEGS AND LEFT FL240 FOR 15000 FT. OUT OF APPROX FL230 THE CTLR ASKED 'WHAT ALT ARE YOU DSNDING TO?' I SAID '15000 FT.' HE REPLIED 'THAT WAS HDG 150 DEGS' AND THAT WE HAD CLARIFIED THAT IN THE READBACK. HE THEN ISSUED A DSCNT CLRNC TO CONTINUE THE DSCNT TO FLT LEVEL 13000 FT. NO FURTHER DISCUSSION. THE PROB WAS IN COM AND THE READBACKS. WE HAD BEEN FLYING ALL NIGHT ALSO; AND THIS WAS THE END OF OUR TRIP. SO FATIGUE WAS ALSO A FACTOR ON OUR PART. SUPPLEMENTAL INFO FROM ACN 483496: AT THIS TIME; I WAS LISTENING TO THE NEW ATIS; AS IT HAD JUST CHANGED AND THE FIELD HAD GONE IMC. THE CAPT (PNF) SWITCHED TO ZHU AND WE WERE DIRECTED TO A 150 DEG HDG AND; WE BELIEVED; A FURTHER DSCNT CLRNC TO 15000 FT. THE CAPT READ BACK THE HDG AND ALT CLRNC AND WE PROCEEDED AS DIRECTED.