ALTDEV ALT OVERSHOT IN CLB AFTER RECEIVING AN AMENDED CLRNC ALT CHANGE.

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FLT RDG-PIT ON JUL/XX/95 TOOK OFF ON RWY 31 FROM READING (RDG) AND CLBED TO 4000 FT. WE CONTACTED HAR APCH/DEP ON 118.25 AND WERE CLRED TO 6000 FT. MY FO READBACK 6000 FT AND SELECTED 6000 FT ON OUR ALT ALERTER. I VERIFIED THE ALT; AFTER IT WAS SET; AS '6000 FT SET.' CLBING THROUGH 5800 FT TO LEVEL AT 6000 FT; THE CTLR ASKED US TO 'SAY ALT.' WE STATED 5800 FT FOR 6000 FT. HE THEN SAID WE HAD ONLY BEEN CLRED TO 5000 FT AND WHEN WE SAID WE HAD READ BACK 6000 FT; HE SAID 'NO YOU WERE CLRED TO 5000 FT AND READ BACK 5000 FT.' WE DIDN'T ARGUE OF COURSE; BUT I STILL BELIEVE THAT WE WERE CLRED TO 6000 FT AND READ BACK 6000 FT BECAUSE I HEARD THE CLRNC; HEARD THE READBACK; AND WATCHED THE ALT BEING SET CORRECTLY IN OUR ACFT. ANYWAY; THERE WAS NO CONFLICT THAT WE KNOW OF; AND NO OTHER ACFT APPEARED ANYWHERE ON OUR TCASII ON THE 25 MI RANGE OR BELOW. SUPPLEMENTAL INFO FROM ACN 311718: AFTER TKOF WHEN DEP SWITCHED US TO ANOTHER APCH FREQ; THE APCH FACILITY GAVE US A MULTIPLE CLRNC INCLUDING A CLRNC TO 5000 FT MSL BUT I READ BACK 6000 FT AND PUT IT IN THE ALT SELECTOR.